Details

analyze1.2s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 85.144043%

sample22.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	10
1	64	10
2	143	10
3	288	10
4	443	10
5	563	10
6	648	10
7	817	10
8	1060	10
9	1066	10
10	1066	10

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 17.9b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.6b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
5×	`flip3-+` `flip-+`
4×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 88

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series51.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
12.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
25.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify68.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	525	728
1	2508	623
2	5001	623

prune162.0ms

Filtered

68 candidates to 100 candidates (-47.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	5	101

Merged error: 0.0b

Counts

101 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

10.6b	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
13.1b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.1b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.1b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
28×	`times-frac`
25×	`add-exp-log`
24×	`associate-r`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`cbrt-prod` `cbrt-div`
18×	`add-cbrt-cube`
15×	`associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 108

Calls

4 calls:

39.0ms	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series49.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
8.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify88.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	701	2328
1	3188	2046
2	5001	1935

prune429.0ms

Filtered

100 candidates to 120 candidates (-20.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	120	5	125

Merged error: 0.0b

Counts

125 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.2b	(* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) (* (+ (* z 0.0692910599291889) 0.4917317610505968) z))
2.6b	(* y (- (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)) (* 0.279195317918525 0.279195317918525)))
23.1b	(/ (* y (- (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)) (* 0.279195317918525 0.279195317918525))) (* (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (- (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
32×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
18×	`associate-*l/`
14×	`prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
10×	`flip3-+` `flip-+`
8×	`frac-times` `add-cube-cbrt` `-un-lft-identity` `associate-r/` `associate-r` `associate-/r/`
7×	`associate-l`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `div-exp` `pow-sqr` `pow-prod-up` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-plus` `associate-/l/` `unswap-sqr`
1×	`pow2` `frac-2neg` `times-frac` `swap-sqr` `clear-num` `associate-/r` `div-inv` `associate-/l` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
13.0ms	(* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) (* (+ (* z 0.0692910599291889) 0.4917317610505968) z))
16.0ms	(* y (- (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)) (* 0.279195317918525 0.279195317918525)))
29.0ms	(/ (* y (- (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)) (* 0.279195317918525 0.279195317918525))) (* (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (- (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.0ms	(* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) (* (+ (* z 0.0692910599291889) 0.4917317610505968) z))
24.0ms	(* y (- (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)) (* 0.279195317918525 0.279195317918525)))
59.0ms	(/ (* y (- (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)) (* 0.279195317918525 0.279195317918525))) (* (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (- (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))

simplify116.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	742	1662
1	4113	1297
2	5002	1297

prune215.0ms

Filtered

76 candidates to 130 candidates (-71.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	130	5	135

Merged error: 0.0b

Counts

135 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

3.6b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
10.8b	(+ (* (* (+ z 6.012459259764103) z) (* (+ z 6.012459259764103) z)) (- (* 3.350343815022304 3.350343815022304) (* (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (pow (* (+ z 6.012459259764103) z) 3) (pow 3.350343815022304 3)))
23.9b	(* (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (pow (* (+ z 6.012459259764103) z) 3) (pow 3.350343815022304 3))) (+ (* (* (+ z 6.012459259764103) z) (* (+ z 6.012459259764103) z)) (- (* 3.350343815022304 3.350343815022304) (* (* (+ z 6.012459259764103) z) 3.350343815022304))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

85×	`associate-*l/`
48×	`frac-add`
43×	`flip3-+` `flip-+`
42×	`frac-times`
34×	`associate-*r/`
24×	`flip3--` `flip--`
20×	`add-exp-log` `add-cbrt-cube`
17×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`associate-l`
11×	`add-cube-cbrt`
10×	`times-frac`
9×	`add-log-exp`
8×	`pow1`
6×	`associate-r` `prod-exp` `cbrt-unprod`
5×	`associate-/r*`
4×	`cbrt-undiv` `div-exp` `associate-/r/`
3×	`sum-cubes` `distribute-lft-out`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `pow-prod-down` `sum-log` `*-commutative` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `sub-neg` `frac-2neg` `diff-log` `clear-num` `associate-/l*`

Counts

4 → 151

Calls

4 calls:

10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.0ms	(+ (* (* (+ z 6.012459259764103) z) (* (+ z 6.012459259764103) z)) (- (* 3.350343815022304 3.350343815022304) (* (* (+ z 6.012459259764103) z) 3.350343815022304)))
20.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (pow (* (+ z 6.012459259764103) z) 3) (pow 3.350343815022304 3)))
36.0ms	(* (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (pow (* (+ z 6.012459259764103) z) 3) (pow 3.350343815022304 3))) (+ (* (* (+ z 6.012459259764103) z) (* (+ z 6.012459259764103) z)) (- (* 3.350343815022304 3.350343815022304) (* (* (+ z 6.012459259764103) z) 3.350343815022304))))

series173.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
6.0ms	(+ (* (* (+ z 6.012459259764103) z) (* (+ z 6.012459259764103) z)) (- (* 3.350343815022304 3.350343815022304) (* (* (+ z 6.012459259764103) z) 3.350343815022304)))
61.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (pow (* (+ z 6.012459259764103) z) 3) (pow 3.350343815022304 3)))
94.0ms	(* (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (pow (* (+ z 6.012459259764103) z) 3) (pow 3.350343815022304 3))) (+ (* (* (+ z 6.012459259764103) z) (* (+ z 6.012459259764103) z)) (- (* 3.350343815022304 3.350343815022304) (* (* (+ z 6.012459259764103) z) 3.350343815022304))))

simplify80.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1544	4588
1	5002	4349

prune720.0ms

Filtered

121 candidates to 163 candidates (-34.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	163	5	168

Merged error: 0.0b

Counts

168 → 5

Details

analyze1.2s

sample22.0ms

simplify66.0ms

prune4.0ms

localize19.0ms

rewrite39.0ms

series51.0ms

simplify68.0ms

prune162.0ms

localize20.0ms

rewrite61.0ms

series49.0ms

simplify88.0ms

prune429.0ms

localize21.0ms

rewrite70.0ms

series94.0ms

simplify116.0ms

prune215.0ms

localize26.0ms

rewrite89.0ms

series173.0ms

simplify80.0ms

prune720.0ms

regimes198.0ms

bsearch1.0ms

Profiling