Details

analyze2.1s (15.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 19 to 19 computations (0% saved)

sample54.0ms (0.4%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
7.0ms	101×	body	128	nan
3.0ms	43×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify136.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	6100	27

prune3.0ms (0%)

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

Error

11.3b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
2.8b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.8b	(/.f64 (.f64 M D) (.f64 2 d))
10.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite216.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

6.1b

Rules

67×	`add-exp-log_binary64_798`
38×	`add-sqr-sqrt_binary64_782`
27×	`prod-exp_binary64_809`
23×	`add-cbrt-cube_binary64_796`
19×	`div-exp_binary64_811` `associate-r_binary64_700`
17×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
15×	`times-frac_binary64_766`
13×	`associate-l_binary64_701`
10×	`pow-exp_binary64_828` `unswap-sqr_binary64_728`
7×	`pow1_binary64_821` `cbrt-unprod_binary64_793` `unpow-prod-down_binary64_839` `sqrt-prod_binary64_776`
5×	`cbrt-undiv_binary64_794`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
3×	`unpow2_binary64_825` `sqr-pow_binary64_732` `associate-*r/_binary64_702` `div-inv_binary64_757`
2×	`pow-to-exp_binary64_829` `*-commutative_binary64_691` `flip3--_binary64_764` `flip--_binary64_735`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `pow-prod-down_binary64_831`

Counts

4 → 116

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
7.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

Compiler

Compiled 3444 to 1962 computations (43% saved)

series1.6s (11.5%)

Error

6.0b

Counts

4 → 71

Calls

4 calls:

551.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
531.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
310.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
126.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4216 to 3713 computations (11.9% saved)

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4982	4087
1	4982	4087

prune213.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	178	9	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	9	188

Error

3.5b

Counts

188 → 9

Compiler

Compiled 4273 to 2231 computations (47.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.8b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
4.8b	(/.f64 (.f64 M D) (.f64 2 d))
4.8b	(/.f64 (.f64 M D) (.f64 2 d))
7.0b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite184.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

69×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
26×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
21×	`div-exp_binary64_811` `cbrt-undiv_binary64_794`
19×	`add-sqr-sqrt_binary64_782`
13×	`add-cube-cbrt_binary64_795` `-un-lft-identity_binary64_760` `times-frac_binary64_766` `associate-r*_binary64_700`
7×	`pow1_binary64_821`
5×	`associate-l_binary64_701`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757`
3×	`sqrt-prod_binary64_776`
2×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704` `sqrt-div_binary64_777`
1×	`pow-prod-down_binary64_831` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `*-commutative_binary64_691` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3--_binary64_764` `flip--_binary64_735` `rem-sqrt-square_binary64_773`

Counts

4 → 109

Calls

4 calls:

12.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))

Compiler

Compiled 3773 to 1881 computations (50.1% saved)

series966.0ms (7%)

Error

2.9b

Counts

4 → 55

Calls

4 calls:

347.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
302.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
135.0ms	(/.f64 (.f64 M D) (.f64 2 d))
131.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3647 to 2843 computations (22% saved)

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5600	2854

prune183.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	159	5	164
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	162	11	173

Error

2.1b

Counts

173 → 11

Compiler

Compiled 4447 to 2123 computations (52.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
2.8b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))
6.1b	(*.f64 (/.f64 M 2) (/.f64 D d))
10.4b	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))

rewrite235.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

2.1b

Rules

67×	`add-exp-log_binary64_798`
58×	`add-sqr-sqrt_binary64_782`
34×	`times-frac_binary64_766`
32×	`associate-r_binary64_700`
30×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
27×	`prod-exp_binary64_809`
23×	`add-cbrt-cube_binary64_796`
22×	`associate-l_binary64_701`
19×	`div-exp_binary64_811`
12×	`unswap-sqr_binary64_728`
10×	`pow-exp_binary64_828`
9×	`pow1_binary64_821`
7×	`cbrt-unprod_binary64_793` `sqrt-prod_binary64_776`
5×	`cbrt-undiv_binary64_794`
4×	`add-log-exp_binary64_799` `associate-*r/_binary64_702` `sqrt-div_binary64_777`
3×	`unpow2_binary64_825` `sqr-pow_binary64_732` `div-inv_binary64_757` `*-commutative_binary64_691`
2×	`pow-to-exp_binary64_829` `pow-prod-down_binary64_831` `flip3--_binary64_764` `flip--_binary64_735`
1×	`unpow-prod-down_binary64_839` `frac-times_binary64_770` `associate-*l/_binary64_703` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773`

Counts

4 → 139

Calls

4 calls:

10.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
10.0ms	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))
7.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))

Compiler

Compiled 4029 to 2284 computations (43.3% saved)

series1.6s (11.3%)

Error

2.1b

Counts

4 → 71

Calls

4 calls:

545.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
518.0ms	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))
302.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))
129.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

Compiler

Compiled 4216 to 3713 computations (11.9% saved)

simplify89.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4984	4391
1	4984	4391

prune227.0ms (1.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	209	12	221

Error

2.1b

Counts

221 → 12

Compiler

Compiled 4903 to 2580 computations (47.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.8b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 1/2 (/.f64 (.f64 M (.f64 D h)) (*.f64 d l))))))
4.8b	(/.f64 (.f64 M D) (.f64 2 d))
5.6b	(.f64 M (.f64 D h))
9.4b	(/.f64 (.f64 M (.f64 D h)) (*.f64 d l))

rewrite126.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

2.1b

Rules

42×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
16×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
10×	`pow1_binary64_821` `div-exp_binary64_811` `cbrt-undiv_binary64_794`
7×	`add-sqr-sqrt_binary64_782`
6×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
4×	`add-log-exp_binary64_799`
3×	`pow-prod-down_binary64_831` `associate-l_binary64_701` `sqrt-prod_binary64_776`
2×	`frac-2neg_binary64_771` `times-frac_binary64_766` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/l_binary64_705` `associate-/r_binary64_704` `sqrt-div_binary64_777`
1×	`associate-r_binary64_700` `*-commutative_binary64_691` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3--_binary64_764` `flip--_binary64_735` `rem-sqrt-square_binary64_773`

Counts

4 → 79

Calls

4 calls:

8.0ms	(/.f64 (.f64 M (.f64 D h)) (*.f64 d l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 1/2 (/.f64 (.f64 M (.f64 D h)) (*.f64 d l))))))
5.0ms	(.f64 M (.f64 D h))

Compiler

Compiled 2683 to 1175 computations (56.2% saved)

series881.0ms (6.4%)

Error

2.1b

Counts

4 → 55

Calls

4 calls:

315.0ms	(/.f64 (.f64 M (.f64 D h)) (*.f64 d l))
296.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 1/2 (/.f64 (.f64 M (.f64 D h)) (*.f64 d l))))))
119.0ms	(/.f64 (.f64 M D) (.f64 2 d))
103.0ms	(.f64 M (.f64 D h))

Compiler

Compiled 3647 to 2851 computations (21.8% saved)

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5000	2169

prune133.0ms (1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	134	12	146

Error

2.1b

Counts

146 → 12

Compiler

Compiled 3430 to 1474 computations (57% saved)

regimes2.1s (15.2%)

Accuracy

Total 4.6b remaining (52.9%)

Threshold costs 0b (0%)

Compiler

Compiled 18682 to 16836 computations (9.9% saved)

bsearch3.0ms (0%)

Compiler: Compiled 13 to 14 computations (-7.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	100
1	74	100

end0.0ms (0%)

sample2.5s (18.3%)

Algorithm

1×

intervals

Results

616.0ms	8000×	body	128	valid
222.0ms	3060×	body	128	nan
100.0ms	1347×	body	128	invalid

Compiler

Compiled 1145 to 1019 computations (11% saved)

Details

analyze2.1s (15.4%)

sample54.0ms (0.4%)

simplify136.0ms (1%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite216.0ms (1.6%)

series1.6s (11.5%)

simplify85.0ms (0.6%)

prune213.0ms (1.5%)

localize15.0ms (0.1%)

rewrite184.0ms (1.3%)

series966.0ms (7%)

simplify62.0ms (0.4%)

prune183.0ms (1.3%)

localize17.0ms (0.1%)

rewrite235.0ms (1.7%)

series1.6s (11.3%)

simplify89.0ms (0.6%)

prune227.0ms (1.6%)

localize20.0ms (0.1%)

rewrite126.0ms (0.9%)

series881.0ms (6.4%)

simplify54.0ms (0.4%)

prune133.0ms (1%)

regimes2.1s (15.2%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.5s (18.3%)

Profiling