Details

analyze851.0ms (10.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1620	124
1	1620	124
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
21.8%	78%	0.1%	9
49.1%	50.7%	0.1%	10
52.7%	47.2%	0.1%	11
52.7%	47.2%	0.1%	12
71.7%	28.2%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 22 to 19 computations (13.6% saved)

sample41.0ms (0.5%)

Algorithm

1×

intervals

Results

23.0ms

256×

body

128

valid

Compiler

Compiled 43 to 40 computations (7% saved)

simplify22.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	453	31
1	453	31

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

19.4b

Counts

2 → 1

Compiler

Compiled 42 to 36 computations (14.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
0.1b	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
3.4b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
18.7b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite240.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

15.3b

Rules

18×	`add-sqr-sqrt_binary64_9989`
15×	`add-exp-log_binary64_10005` `add-cbrt-cube_binary64_10003`
14×	`*-un-lft-identity_binary64_9967`
12×	`add-cube-cbrt_binary64_10002`
10×	`pow1_binary64_10028` `associate-l_binary64_9908`
9×	`associate-r_binary64_9907`
5×	`flip3-+_binary64_9970` `flip-+_binary64_9941`
4×	`prod-exp_binary64_10016` `add-log-exp_binary64_10006` `cbrt-unprod_binary64_10000` `associate-r/_binary64_9909` `associate-l/_binary64_9910`
3×	`times-frac_binary64_9973` `associate-/r_binary64_9911` `pow-prod-down_binary64_10038` `unswap-sqr_binary64_9935` `-commutative_binary64_9898`
2×	`div-exp_binary64_10018` `cbrt-undiv_binary64_10001` `associate-/l/_binary64_9914` `associate-/r/_binary64_9913`
1×	`frac-2neg_binary64_9978` `clear-num_binary64_9966` `div-inv_binary64_9964` `associate-/l*_binary64_9912` `distribute-rgt-in_binary64_9917` `distribute-lft-in_binary64_9916` `distribute-lft-out_binary64_9918`

Counts

4 → 88

Calls

4 calls:

26.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
18.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
11.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
7.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

Compiler

Compiled 2735 to 2008 computations (26.6% saved)

series568.0ms (7.2%)

Error

0.0b

Counts

4 → 39

Calls

4 calls:

237.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
192.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
46.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
43.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

Compiler

Compiled 1909 to 1525 computations (20.1% saved)

simplify108.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4905	2207
1	4905	2207

prune213.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	123	5	128

Error

0.0b

Counts

128 → 5

Compiler

Compiled 3262 to 2367 computations (27.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 x (*.f64 4992947066835229/72057594037927936 y))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

3×	`add-log-exp_binary64_10006`
1×	`sum-log_binary64_10058` `pow1_binary64_10028` `add-exp-log_binary64_10005` `add-cbrt-cube_binary64_10003` `add-cube-cbrt_binary64_10002` `add-sqr-sqrt_binary64_9989` `flip3-+_binary64_9970` `*-un-lft-identity_binary64_9967` `flip-+_binary64_9941` `+-commutative_binary64_9897`

Counts

1 → 11

Calls

1 calls:

5.0ms

(+.f64 x (*.f64 4992947066835229/72057594037927936 y))

Compiler

Compiled 136 to 96 computations (29.4% saved)

series64.0ms (0.8%)

Error

0.0b

Counts

1 → 12

Calls

1 calls:

58.0ms

(+.f64 x (*.f64 4992947066835229/72057594037927936 y))

Compiler

Compiled 114 to 123 computations (-7.9% saved)

simplify155.0ms (2%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	4817	193
1	4817	193

prune36.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	22	1	23
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	22	6	28

Error

Counts

28 → 6

Compiler

Compiled 256 to 190 computations (25.8% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.2b	(.f64 (/.f64 y (sqrt.f64 (+.f64 7544303578448747/2251799813685248 (.f64 z (+.f64 z 1692356830115869/281474976710656))))) (/.f64 (+.f64 5029535718965825/18014398509481984 (.f64 z (+.f64 4429125951667411/9007199254740992 (.f64 4992947066835229/72057594037927936 z)))) (sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656))))))
14.2b	(sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656))))
14.2b	(sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656))))
14.3b	(/.f64 (+.f64 5029535718965825/18014398509481984 (.f64 z (+.f64 4429125951667411/9007199254740992 (.f64 4992947066835229/72057594037927936 z)))) (sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656)))))

rewrite603.0ms (7.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

79×	`add-sqr-sqrt_binary64_9989`
66×	`times-frac_binary64_9973`
47×	`add-cube-cbrt_binary64_10002` `*-un-lft-identity_binary64_9967`
42×	`sqrt-prod_binary64_9983`
24×	`associate-l_binary64_9908` `associate-r_binary64_9907`
18×	`add-exp-log_binary64_10005` `add-cbrt-cube_binary64_10003`
10×	`sqrt-div_binary64_9984`
9×	`unswap-sqr_binary64_9935`
8×	`pow1_binary64_10028`
6×	`flip3-+_binary64_9970` `flip-+_binary64_9941` `associate-/r/_binary64_9913` `associate-/r*_binary64_9911`
5×	`div-exp_binary64_10018` `cbrt-undiv_binary64_10001`
4×	`add-log-exp_binary64_10006` `prod-exp_binary64_10016` `cbrt-unprod_binary64_10000`
3×	`div-inv_binary64_9964` `associate-/l*_binary64_9912`
2×	`associate-/l/_binary64_9914` `pow1/2_binary64_10047` `sqrt-pow1_binary64_9985` `rem-sqrt-square_binary64_9980`
1×	`frac-2neg_binary64_9978` `clear-num_binary64_9966` `pow-prod-down_binary64_10038` `frac-times_binary64_9977` `associate-l/_binary64_9910` `associate-r/_binary64_9909` `*-commutative_binary64_9898`

Counts

4 → 150

Calls

4 calls:

27.0ms	(.f64 (/.f64 y (sqrt.f64 (+.f64 7544303578448747/2251799813685248 (.f64 z (+.f64 z 1692356830115869/281474976710656))))) (/.f64 (+.f64 5029535718965825/18014398509481984 (.f64 z (+.f64 4429125951667411/9007199254740992 (.f64 4992947066835229/72057594037927936 z)))) (sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656))))))
8.0ms	(/.f64 (+.f64 5029535718965825/18014398509481984 (.f64 z (+.f64 4429125951667411/9007199254740992 (.f64 4992947066835229/72057594037927936 z)))) (sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656)))))
3.0ms	(sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656))))
3.0ms	(sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656))))

Compiler

Compiled 7390 to 5634 computations (23.8% saved)

series537.0ms (6.8%)

Error

Counts

4 → 45

Calls

4 calls:

246.0ms	(.f64 (/.f64 y (sqrt.f64 (+.f64 7544303578448747/2251799813685248 (.f64 z (+.f64 z 1692356830115869/281474976710656))))) (/.f64 (+.f64 5029535718965825/18014398509481984 (.f64 z (+.f64 4429125951667411/9007199254740992 (.f64 4992947066835229/72057594037927936 z)))) (sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656))))))
84.0ms	(/.f64 (+.f64 5029535718965825/18014398509481984 (.f64 z (+.f64 4429125951667411/9007199254740992 (.f64 4992947066835229/72057594037927936 z)))) (sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656)))))
68.0ms	(sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656))))
56.0ms	(sqrt.f64 (+.f64 7544303578448747/2251799813685248 (*.f64 z (+.f64 z 1692356830115869/281474976710656))))

Compiler

Compiled 2765 to 2277 computations (17.6% saved)

simplify166.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5723	6773

prune560.0ms (7.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	195	6	201

Error

Counts

201 → 6

Compiler

Compiled 7805 to 5896 computations (24.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 5029535718965825/60354428627589976 (*.f64 z -632405738649506141492951023683/227666065935178277118539623480036))
0.0b	(+.f64 x (.f64 y (+.f64 5029535718965825/60354428627589976 (.f64 z -632405738649506141492951023683/227666065935178277118539623480036))))
0.2b	(.f64 y (+.f64 5029535718965825/60354428627589976 (.f64 z -632405738649506141492951023683/227666065935178277118539623480036)))
0.3b	(*.f64 z -632405738649506141492951023683/227666065935178277118539623480036)

rewrite97.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`add-sqr-sqrt_binary64_9989`
8×	`pow1_binary64_10028` `add-exp-log_binary64_10005` `add-log-exp_binary64_10006` `add-cbrt-cube_binary64_10003` `add-cube-cbrt_binary64_10002` `*-un-lft-identity_binary64_9967`
6×	`associate-l_binary64_9908` `associate-r_binary64_9907`
3×	`flip3-+_binary64_9970` `flip-+_binary64_9941`
2×	`pow-prod-down_binary64_10038` `prod-exp_binary64_10016` `cbrt-unprod_binary64_10000` `unswap-sqr_binary64_9935` `-commutative_binary64_9898` `distribute-rgt-in_binary64_9917` `distribute-lft-in_binary64_9916` `associate-r/_binary64_9909` `sum-log_binary64_10058` `associate-+r+_binary64_9899` `+-commutative_binary64_9897`

Counts

4 → 64

Calls

4 calls:

7.0ms	(*.f64 z -632405738649506141492951023683/227666065935178277118539623480036)
6.0ms	(.f64 y (+.f64 5029535718965825/60354428627589976 (.f64 z -632405738649506141492951023683/227666065935178277118539623480036)))
3.0ms	(+.f64 x (.f64 y (+.f64 5029535718965825/60354428627589976 (.f64 z -632405738649506141492951023683/227666065935178277118539623480036))))
3.0ms	(+.f64 5029535718965825/60354428627589976 (*.f64 z -632405738649506141492951023683/227666065935178277118539623480036))

Compiler

Compiled 1028 to 746 computations (27.4% saved)

series402.0ms (5.1%)

Error

Counts

4 → 36

Calls

4 calls:

209.0ms	(+.f64 x (.f64 y (+.f64 5029535718965825/60354428627589976 (.f64 z -632405738649506141492951023683/227666065935178277118539623480036))))
124.0ms	(.f64 y (+.f64 5029535718965825/60354428627589976 (.f64 z -632405738649506141492951023683/227666065935178277118539623480036)))
31.0ms	(+.f64 5029535718965825/60354428627589976 (*.f64 z -632405738649506141492951023683/227666065935178277118539623480036))
17.0ms	(*.f64 z -632405738649506141492951023683/227666065935178277118539623480036)

Compiler

Compiled 801 to 670 computations (16.4% saved)

simplify87.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5263	1056

prune89.0ms (1.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	100	6	106

Error

Counts

106 → 6

Compiler

Compiled 1190 to 832 computations (30.1% saved)

regimes901.0ms (11.4%)

Accuracy

Total 0.2b remaining (99.2%)

Threshold costs 0.2b (99.2%)

Compiler

Compiled 5648 to 4829 computations (14.5% saved)

bsearch55.0ms (0.7%)

Steps

Iters	Range		Point
10	9.416312076425774e-09	48.680051193511154	48.17602907496802
5	-2.5431286576031824e+36	-9.84199984016058e+35	-9.990746456204017e+35

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	88	73
1	88	73

end0.0ms (0%)

sample2.0s (25.8%)

Algorithm

1×

intervals

Results

514.0ms

8000×

body

128

valid

Compiler

Compiled 1215 to 1027 computations (15.5% saved)

Details

analyze851.0ms (10.7%)

sample41.0ms (0.5%)

simplify22.0ms (0.3%)

prune5.0ms (0.1%)

localize15.0ms (0.2%)

rewrite240.0ms (3%)

series568.0ms (7.2%)

simplify108.0ms (1.4%)

prune213.0ms (2.7%)

localize5.0ms (0.1%)

rewrite17.0ms (0.2%)

series64.0ms (0.8%)

simplify155.0ms (2%)

prune36.0ms (0.5%)

localize23.0ms (0.3%)

rewrite603.0ms (7.6%)

series537.0ms (6.8%)

simplify166.0ms (2.1%)

prune560.0ms (7.1%)

localize13.0ms (0.2%)

rewrite97.0ms (1.2%)

series402.0ms (5.1%)

simplify87.0ms (1.1%)

prune89.0ms (1.1%)

regimes901.0ms (11.4%)

bsearch55.0ms (0.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (25.8%)

Profiling