Profiling results ----------------- Total cpu time observed: 7708ms (out of 7884ms) Number of samples taken: 34 (once every 227ms) ======================================================================== Caller Idx Total Self Name+src Local% ms(pct) ms(pct) Callee ======================================================================== [1] 7708(100.0%) 0(0.0%) ??? ...lects/racket/private/more-scheme.rkt:261:28 profile-thunk16 [9] 100.0% ------------------------------------------------------------------------ location-do [2] 21.3% ??? [67] 78.7% [2] 1824(23.7%) 0(0.0%) location-do ...herbie/master/src/programs.rkt:64:0 ??? [67] 62.8% location-do [2] 21.3% loop [13] 15.8% ------------------------------------------------------------------------ ??? [67] 100.0% [3] 1824(23.7%) 0(0.0%) approximate9 ...ie/master/src/core/taylor.rkt:12:0 loop [10] 100.0% ------------------------------------------------------------------------ hash-ref! [73] 100.0% [4] 984(12.8%) 0(0.0%) ??? ...es/herbie/master/src/core/taylor.rkt:291:26 for-loop [11] 100.0% ------------------------------------------------------------------------ hash-ref! [73] 100.0% [5] 984(12.8%) 0(0.0%) ??? ...es/herbie/master/src/core/taylor.rkt:301:23 for-loop [12] 100.0% ------------------------------------------------------------------------ matcher [78] 100.0% [6] 208(2.7%) 0(0.0%) ??? ...s/herbie/master/src/core/matcher.rkt:130:11 for-loop [14] 100.0% ------------------------------------------------------------------------ loop [106] 100.0% [7] 200(2.6%) 0(0.0%) syntax-e (unknown source) syntax-e/no-taint [16] 100.0% ------------------------------------------------------------------------ loop [106] 100.0% [8] 200(2.6%) 0(0.0%) dispatch-transformer41 (unknown source) apply-transformer52 [15] 100.0% ------------------------------------------------------------------------ ??? [1] 100.0% [9] 7708(100.0%) 0(0.0%) profile-thunk16 ...e/pkgs/profile-lib/main.rkt:9:0 run [17] 100.0% ------------------------------------------------------------------------ approximate9 [3] 100.0% [10] 1824(23.7%) 0(0.0%) loop ...ies/herbie/master/src/core/taylor.rkt:87:4 ??? [67] 100.0% ------------------------------------------------------------------------ ??? [4] 100.0% [11] 984(12.8%) 0(0.0%) for-loop ...rbie/master/src/core/taylor.rkt:291:52 hash-ref! [73] 100.0% ------------------------------------------------------------------------ ??? [5] 100.0% [12] 984(12.8%) 0(0.0%) for-loop ...rbie/master/src/core/taylor.rkt:304:27 hash-ref! [73] 79.7% simplify [18] 20.3% ------------------------------------------------------------------------ location-do [2] 100.0% [13] 578(7.5%) 0(0.0%) loop ...htlies/herbie/master/src/programs.rkt:73:4 ??? [67] 100.0% ------------------------------------------------------------------------ ??? [6] 100.0% [14] 208(2.7%) 0(0.0%) for-loop ...bie/master/src/core/matcher.rkt:132:15 matcher [78] 100.0% ------------------------------------------------------------------------ dispatch-transformer41 [8] 100.0% [15] 200(2.6%) 0(0.0%) apply-transformer52 (unknown source) apply-transformer-in-context [19]100.0% ------------------------------------------------------------------------ syntax-e [7] 100.0% [16] 200(2.6%) 0(0.0%) syntax-e/no-taint (unknown source) loop [106] 100.0% ------------------------------------------------------------------------ profile-thunk16 [9] 100.0% [17] 7708(100.0%) 0(0.0%) run ...et-7.5/share/pkgs/profile-lib/main.rkt:39:2 .../more-scheme.rkt:261:28 [20] 100.0% ------------------------------------------------------------------------ for-loop [12] 11.0% hash-ref! [73] 89.0% [18] 1824(23.7%) 0(0.0%) simplify ...herbie/master/src/core/reduce.rkt:16:0 parse-loop80 [21] 89.0% f67 [22] 11.0% ------------------------------------------------------------------------ apply-transformer52 [15] 100.0% [19] 200(2.6%) 0(0.0%) apply-transformer-in-context (unknown source) ??? [23] 100.0% ------------------------------------------------------------------------ for-loop [83] 5.2% run [17] 94.8% [20] 7708(100.0%) 0(0.0%) .../more-scheme.rkt:261:28 (unknown source) run-improve47 [24] 58.7% prepare-points-intervals [25] 25.7% ??? [39] 5.2% oracle-error [27] 5.2% errors [74] 2.7% get-final-combination [29] 2.6% ------------------------------------------------------------------------ simplify [18] 100.0% [21] 1624(21.1%) 0(0.0%) parse-loop80 (unknown source) eval-const-expr [26] 100.0% ------------------------------------------------------------------------ simplify [18] 100.0% [22] 200(2.6%) 200(2.6%) f67 (unknown source) ------------------------------------------------------------------------ apply-transformer-in-context [19]100.0% [23] 200(2.6%) 0(0.0%) ??? ...collects/racket/private/qq-and-or.rkt:155:9 ??? [28] 100.0% ------------------------------------------------------------------------ .../more-scheme.rkt:261:28 [20] 100.0% [24] 4718(61.2%) 0(0.0%) run-improve47 ...bie/master/src/mainloop.rkt:346:0 for-loop [30] 95.6% simplify! [40] 4.4% ------------------------------------------------------------------------ .../more-scheme.rkt:261:28 [20] 100.0% [25] 1980(25.7%) 0(0.0%) prepare-points-intervals ...r/src/points.rkt:110:0 loop [31] 100.0% ------------------------------------------------------------------------ parse-loop80 [21] 100.0% [26] 1624(21.1%) 0(0.0%) eval-const-expr ...e/master/src/programs.rkt:118:0 temp85_0 [91] 76.7% loop [106] 23.3% ------------------------------------------------------------------------ .../more-scheme.rkt:261:28 [20] 100.0% [27] 400(5.2%) 0(0.0%) oracle-error ...herbie/master/src/points.rkt:188:0 for-loop [32] 100.0% ------------------------------------------------------------------------ ??? [23] 100.0% [28] 200(2.6%) 0(0.0%) ??? ...ollects/racket/private/qq-and-or.rkt:164:21 syntax->list [33] 100.0% ------------------------------------------------------------------------ .../more-scheme.rkt:261:28 [20] 100.0% [29] 200(2.6%) 0(0.0%) get-final-combination ...er/src/mainloop.rkt:371:0 infer-splitpoints [34] 100.0% ------------------------------------------------------------------------ run-improve47 [24] 100.0% [30] 4510(58.5%) 0(0.0%) for-loop ...s/herbie/master/src/mainloop.rkt:365:4 run-iter! [35] 100.0% ------------------------------------------------------------------------ prepare-points-intervals [25] 100.0% [31] 1980(25.7%) 0(0.0%) loop ...ghtlies/herbie/master/src/points.rkt:123:4 loop [36] 90.5% ??? [38] 9.5% ------------------------------------------------------------------------ oracle-error [27] 100.0% [32] 400(5.2%) 0(0.0%) for-loop ...ies/herbie/master/src/points.rkt:189:2 loop [106] 100.0% ------------------------------------------------------------------------ ??? [28] 100.0% [33] 200(2.6%) 0(0.0%) syntax->list (unknown source) loop [106] 100.0% ------------------------------------------------------------------------ get-final-combination [29] 100.0% [34] 200(2.6%) 0(0.0%) infer-splitpoints ...ter/src/core/regimes.rkt:34:0 for-loop [37] 100.0% ------------------------------------------------------------------------ for-loop [30] 100.0% [35] 4510(58.5%) 0(0.0%) run-iter! .../herbie/master/src/mainloop.rkt:327:0 gen-series! [41] 40.4% simplify! [40] 36.8% finalize-iter! [42] 13.8% gen-rewrites! [43] 4.6% choose-best-alt! [45] 4.3% ------------------------------------------------------------------------ loop [31] 100.0% [36] 1792(23.2%) 400(5.2%) loop ...ightlies/herbie/master/src/points.rkt:81:2 ??? [39] 77.7% ------------------------------------------------------------------------ infer-splitpoints [34] 100.0% [37] 200(2.6%) 0(0.0%) for-loop ...erbie/master/src/core/regimes.rkt:47:6 option-on-expr [44] 100.0% ------------------------------------------------------------------------ loop [31] 100.0% [38] 188(2.4%) 0(0.0%) ??? ...ightlies/herbie/master/src/points.rkt:106:2 ??? [67] 100.0% ------------------------------------------------------------------------ loop [106] 8.3% .../more-scheme.rkt:261:28 [20] 33.6% loop [36] 58.1% [39] 2396(31.1%) 202(2.6%) ??? ...htlies/herbie/master/src/programs.rkt:115:2 ??? [48] 33.5% ??? [67] 33.2% ??? [50] 24.9% ------------------------------------------------------------------------ run-improve47 [24] 11.1% run-iter! [35] 88.9% [40] 1868(24.2%) 0(0.0%) simplify! .../herbie/master/src/mainloop.rkt:224:0 egraph-run [46] 100.0% ------------------------------------------------------------------------ run-iter! [35] 100.0% [41] 1824(23.7%) 0(0.0%) gen-series! ...erbie/master/src/mainloop.rkt:160:0 for-loop [47] 100.0% ------------------------------------------------------------------------ run-iter! [35] 100.0% [42] 624(8.1%) 0(0.0%) finalize-iter! ...ie/master/src/mainloop.rkt:278:0 ??? [49] 100.0% ------------------------------------------------------------------------ run-iter! [35] 100.0% [43] 208(2.7%) 0(0.0%) gen-rewrites! ...bie/master/src/mainloop.rkt:183:0 for-loop [51] 100.0% ------------------------------------------------------------------------ for-loop [37] 100.0% [44] 200(2.6%) 0(0.0%) option-on-expr ...aster/src/core/regimes.rkt:126:0 for-loop [52] 100.0% ------------------------------------------------------------------------ run-iter! [35] 100.0% [45] 194(2.5%) 0(0.0%) choose-best-alt! .../master/src/mainloop.rkt:117:0 ...ow-val-first.rkt:486:18 [53] 100.0% ------------------------------------------------------------------------ simplify! [40] 100.0% [46] 1868(24.2%) 0(0.0%) egraph-run ...bie/master/src/core/eggmath.rkt:51:0 egraph-add-exprs [54] 100.0% ------------------------------------------------------------------------ gen-series! [41] 100.0% [47] 1824(23.7%) 0(0.0%) for-loop ...s/herbie/master/src/mainloop.rkt:167:7 taylor-alt [55] 100.0% ------------------------------------------------------------------------ ??? [39] 100.0% [48] 802(10.4%) 602(7.8%) ??? .../herbie/master/src/syntax/syntax.rkt:214:17 list-member? [58] 24.9% ------------------------------------------------------------------------ finalize-iter! [42] 100.0% [49] 624(8.1%) 0(0.0%) ??? ...contract/private/arrow-val-first.rkt:486:18 for-loop [56] 100.0% ------------------------------------------------------------------------ ??? [39] 100.0% [50] 596(7.7%) 196(2.5%) ??? ...tract/private/arrow-higher-order.rkt:379:33 ival-sub [59] 33.6% ival-add [60] 33.6% ------------------------------------------------------------------------ gen-rewrites! [43] 100.0% [51] 208(2.7%) 0(0.0%) for-loop .../herbie/master/src/mainloop.rkt:191:11 rewrite-expression-head20 [57] 100.0% ------------------------------------------------------------------------ option-on-expr [44] 100.0% [52] 200(2.6%) 0(0.0%) for-loop ...rbie/master/src/core/regimes.rkt:136:4 errors [74] 100.0% ------------------------------------------------------------------------ choose-best-alt! [45] 100.0% [53] 194(2.5%) 0(0.0%) ...ow-val-first.rkt:486:18 (unknown source) ??? [61] 100.0% ------------------------------------------------------------------------ egraph-run [46] 100.0% [54] 1868(24.2%) 0(0.0%) egraph-add-exprs ...ter/src/core/eggmath.rkt:113:0 ??? [62] 100.0% ------------------------------------------------------------------------ for-loop [47] 100.0% [55] 1824(23.7%) 0(0.0%) taylor-alt ...herbie/master/src/mainloop.rkt:146:0 for-loop [63] 100.0% ------------------------------------------------------------------------ ??? [49] 100.0% [56] 624(8.1%) 0(0.0%) for-loop ...bie/master/src/core/alt-table.rkt:55:2 atab-add-altn [64] 64.1% errors [74] 35.9% ------------------------------------------------------------------------ for-loop [51] 100.0% [57] 208(2.7%) 0(0.0%) rewrite-expression-head20 ...core/matcher.rkt:87:0 rewriter [65] 100.0% ------------------------------------------------------------------------ ??? [48] 100.0% [58] 200(2.6%) 200(2.6%) list-member? ...llects/racket/private/set.rkt:24:0 ------------------------------------------------------------------------ ??? [50] 100.0% [59] 200(2.6%) 0(0.0%) ival-sub ...erbie/master/src/biginterval.rkt:107:0 bfadd [84] 100.0% ------------------------------------------------------------------------ ??? [50] 100.0% [60] 200(2.6%) 0(0.0%) ival-add ...erbie/master/src/biginterval.rkt:101:0 bfadd [84] 100.0% ------------------------------------------------------------------------ ...ow-val-first.rkt:486:18 [53] 100.0% [61] 194(2.5%) 0(0.0%) ??? ...s/herbie/master/src/core/alt-table.rkt:58:0 loop [66] 100.0% ------------------------------------------------------------------------ egraph-add-exprs [54] 100.0% [62] 1868(24.2%) 0(0.0%) ??? ...es/herbie/master/src/core/simplify.rkt:72:6 for-loop [68] 88.4% egg-run-rules [69] 11.6% ------------------------------------------------------------------------ taylor-alt [55] 100.0% [63] 1824(23.7%) 0(0.0%) for-loop ...s/herbie/master/src/mainloop.rkt:152:6 ??? [67] 100.0% ------------------------------------------------------------------------ for-loop [56] 100.0% [64] 400(5.2%) 0(0.0%) atab-add-altn ...ster/src/core/alt-table.rkt:203:0 override-at-pnts [71] 50.0% errors [74] 50.0% ------------------------------------------------------------------------ rewrite-expression-head20 [57] 33.3% matcher [78] 66.7% [65] 208(2.7%) 0(0.0%) rewriter ...erbie/master/src/core/matcher.rkt:90:2 for-loop [70] 100.0% ------------------------------------------------------------------------ ??? [61] 100.0% [66] 194(2.5%) 0(0.0%) loop .../racket-7.5/collects/racket/list.rkt:751:4 ??? [72] 100.0% ------------------------------------------------------------------------ ??? [38] 6.7% loop [13] 6.9% location-do [2] 14.8% loop [10] 21.7% for-loop [63] 21.7% ??? [39] 28.3% [67] 2808(36.4%) 0(0.0%) ??? ...tract/private/arrow-higher-order.rkt:375:33 location-do [2] 21.7% approximate9 [3] 21.7% hash-ref! [73] 21.7% ival-mult [75] 21.4% mk-ival [80] 6.9% sample-multi-bounded [81] 6.7% ------------------------------------------------------------------------ ??? [62] 100.0% [68] 1652(21.4%) 1652(21.4%) for-loop ...rbie/master/src/core/simplify.rkt:91:2 ------------------------------------------------------------------------ ??? [62] 100.0% [69] 216(2.8%) 0(0.0%) egg-run-rules ...master/src/core/simplify.rkt:78:0 make-ffi-rules [76] 100.0% ------------------------------------------------------------------------ rewriter [65] 100.0% [70] 208(2.7%) 0(0.0%) for-loop ...erbie/master/src/core/matcher.rkt:92:4 matcher [78] 66.7% for-loop [77] 33.3% ------------------------------------------------------------------------ atab-add-altn [64] 100.0% [71] 200(2.6%) 0(0.0%) override-at-pnts ...r/src/core/alt-table.rkt:138:0 for-loop [79] 100.0% ------------------------------------------------------------------------ loop [66] 100.0% [72] 194(2.5%) 0(0.0%) ??? ...tlies/herbie/master/src/mainloop.rkt:114:10 errors [74] 100.0% ------------------------------------------------------------------------ ??? [85] 7.1% for-loop [12] 12.5% for-loop [11] 18.9% ??? [82] 30.8% ??? [67] 30.8% [73] 1824(23.7%) 0(0.0%) hash-ref! .../racket/private/more-scheme.rkt:376:2 ??? [82] 30.8% simplify [18] 27.1% ??? [4] 18.9% ??? [5] 16.1% ??? [85] 7.1% ------------------------------------------------------------------------ ??? [72] 15.8% atab-add-altn [64] 16.3% for-loop [52] 16.3% for-loop [56] 18.2% .../more-scheme.rkt:261:28 [20] 33.4% [74] 1228(15.9%) 0(0.0%) errors ...tlies/herbie/master/src/points.rkt:201:0 for-loop [83] 83.7% eval-prog [88] 16.3% ------------------------------------------------------------------------ ??? [67] 100.0% [75] 602(7.8%) 0(0.0%) ival-mult ...rbie/master/src/biginterval.rkt:119:0 bfadd [84] 100.0% ------------------------------------------------------------------------ egg-run-rules [69] 100.0% [76] 216(2.8%) 0(0.0%) make-ffi-rules ...master/src/core/eggmath.rkt:30:0 for-loop [86] 100.0% ------------------------------------------------------------------------ for-loop [70] 100.0% [77] 208(2.7%) 0(0.0%) for-loop ...erbie/master/src/core/matcher.rkt:99:8 fix-up-variables [87] 100.0% ------------------------------------------------------------------------ for-loop [14] 50.0% for-loop [70] 50.0% [78] 208(2.7%) 0(0.0%) matcher ...erbie/master/src/core/matcher.rkt:118:2 ??? [6] 50.0% rewriter [65] 50.0% ------------------------------------------------------------------------ override-at-pnts [71] 100.0% [79] 200(2.6%) 200(2.6%) for-loop ...e/master/src/core/alt-table.rkt:139:22 ------------------------------------------------------------------------ ??? [67] 100.0% [80] 194(2.5%) 0(0.0%) mk-ival .../herbie/master/src/biginterval.rkt:65:0 bf [89] 100.0% ------------------------------------------------------------------------ ??? [67] 100.0% [81] 188(2.4%) 0(0.0%) sample-multi-bounded ...master/src/points.rkt:15:0 random-ranges [90] 100.0% ------------------------------------------------------------------------ hash-ref! [73] 100.0% [82] 1824(23.7%) 0(0.0%) ??? ...ies/herbie/master/src/core/taylor.rkt:45:15 hash-ref! [73] 100.0% ------------------------------------------------------------------------ errors [74] 100.0% [83] 1028(13.3%) 224(2.9%) for-loop ...ies/herbie/master/src/points.rkt:203:2 .../more-scheme.rkt:261:28 [20] 78.2% ------------------------------------------------------------------------ ival-add [60] 20.0% ival-sub [59] 20.0% ival-mult [75] 60.1% [84] 1002(13.0%) 0(0.0%) bfadd ...-lib/math/private/bigfloat/mpfr.rkt:835:4 ??? [92] 59.5% new-mpfr [93] 40.5% ------------------------------------------------------------------------ hash-ref! [73] 100.0% [85] 440(5.7%) 0(0.0%) ??? ...es/herbie/master/src/core/taylor.rkt:344:33 hash-ref! [73] 100.0% ------------------------------------------------------------------------ make-ffi-rules [76] 100.0% [86] 216(2.8%) 216(2.8%) for-loop ...erbie/master/src/core/eggmath.rkt:31:2 ------------------------------------------------------------------------ for-loop [77] 100.0% [87] 208(2.7%) 0(0.0%) fix-up-variables ...ter/src/core/matcher.rkt:111:2 pattern-substitute [94] 100.0% ------------------------------------------------------------------------ errors [74] 100.0% [88] 200(2.6%) 0(0.0%) eval-prog ...s/herbie/master/src/programs.rkt:83:0 temp85_0 [91] 100.0% ------------------------------------------------------------------------ mk-ival [80] 100.0% [89] 194(2.5%) 194(2.5%) bf ...ath-lib/math/private/bigfloat/mpfr.rkt:615:2 ------------------------------------------------------------------------ sample-multi-bounded [81] 100.0% [90] 188(2.4%) 0(0.0%) random-ranges ...erbie/master/src/common.rkt:171:0 cons/c [95] 100.0% ------------------------------------------------------------------------ eval-prog [88] 13.8% eval-const-expr [26] 86.2% [91] 1446(18.8%) 0(0.0%) temp85_0 (unknown source) compile15 [96] 100.0% ------------------------------------------------------------------------ bfadd [84] 100.0% [92] 596(7.7%) 596(7.7%) ??? /opt/racket-7.5/collects/ffi/unsafe.rkt:938:4 ------------------------------------------------------------------------ bfadd [84] 100.0% [93] 406(5.3%) 406(5.3%) new-mpfr ...b/math/private/bigfloat/mpfr.rkt:348:0 ------------------------------------------------------------------------ fix-up-variables [87] 100.0% [94] 208(2.7%) 208(2.7%) pattern-substitute ...er/src/core/matcher.rkt:46:0 ------------------------------------------------------------------------ random-ranges [90] 100.0% [95] 188(2.4%) 0(0.0%) cons/c .../racket/contract/private/guts.rkt:500:15 coerce-contract [97] 100.0% ------------------------------------------------------------------------ temp85_0 [91] 100.0% [96] 1446(18.8%) 0(0.0%) compile15 (unknown source) temp91_0 [98] 100.0% ------------------------------------------------------------------------ cons/c [95] 100.0% [97] 188(2.4%) 0(0.0%) coerce-contract ...contract/private/guts.rkt:307:0 coerce-contract/f [99] 100.0% ------------------------------------------------------------------------ compile15 [96] 100.0% [98] 1446(18.8%) 0(0.0%) temp91_0 (unknown source) temp118_0 [100] 100.0% ------------------------------------------------------------------------ coerce-contract [97] 100.0% [99] 188(2.4%) 0(0.0%) coerce-contract/f ...ntract/private/guts.rkt:372:0 coerce-simple-value [101] 100.0% ------------------------------------------------------------------------ temp91_0 [98] 100.0% [100] 1446(18.8%) 0(0.0%) temp118_0 (unknown source) expand-capturing-lifts [102] 100.0% ------------------------------------------------------------------------ coerce-contract/f [99] 100.0% [101] 188(2.4%) 188(2.4%) coerce-simple-value ...ract/private/guts.rkt:385:0 ------------------------------------------------------------------------ loop [106] 20.7% temp118_0 [100] 79.3% [102] 1824(23.7%) 0(0.0%) expand-capturing-lifts (unknown source) lambda-clause-expander [103] 79.3% loop [106] 20.7% ------------------------------------------------------------------------ expand-capturing-lifts [102] 100.0% [103] 1446(18.8%) 0(0.0%) lambda-clause-expander (unknown source) finish-bodys [104] 86.2% loop [106] 13.8% ------------------------------------------------------------------------ lambda-clause-expander [103] 40.2% for-loop [105] 59.8% [104] 1246(16.2%) 200(2.6%) finish-bodys (unknown source) for-loop [105] 94.6% ------------------------------------------------------------------------ for-loop [105] 3.2% finish-bodys [104] 96.8% [105] 1246(16.2%) 400(5.2%) for-loop (unknown source) finish-bodys [104] 62.3% loop [106] 16.5% expand-body7 [107] 9.6% for-loop [105] 3.2% expand-identifier [108] 1.6% ------------------------------------------------------------------------ for-loop [105] 4.3% syntax-e/no-taint [16] 5.6% syntax->list [33] 5.6% lambda-clause-expander [103] 5.6% loop [106] 13.0% expand-capturing-lifts [102] 16.0% eval-const-expr [26] 16.0% for-loop [32] 33.8% [106] 1184(15.4%) 584(7.6%) loop (unknown source) ??? [109] 16.9% ??? [39] 16.9% expand-capturing-lifts [102] 16.0% loop [106] 13.0% dispatch-transformer41 [8] 5.6% syntax-e [7] 5.6% gf [110] 5.6% ------------------------------------------------------------------------ for-loop [105] 100.0% [107] 240(3.1%) 240(3.1%) expand-body7 (unknown source) ------------------------------------------------------------------------ for-loop [105] 100.0% [108] 200(2.6%) 200(2.6%) expand-identifier (unknown source) ------------------------------------------------------------------------ loop [106] 100.0% [109] 200(2.6%) 200(2.6%) ??? ...ghtlies/herbie/master/src/points.rkt:190:26 ------------------------------------------------------------------------ loop [106] 100.0% [110] 200(2.6%) 200(2.6%) gf (unknown source) ------------------------------------------------------------------------