Details

analyze2.0s (11.7%)

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
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 34 to 30 computations (11.8% saved)

sample71.0ms (0.4%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
17.0ms	178×	body	128	nan

Compiler

Compiled 67 to 66 computations (1.5% saved)

simplify197.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4980	44
1	4980	44

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 4.5b

Counts

2 → 1

Compiler

Compiled 58 to 50 computations (13.8% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.3b	(/.f64 2/3 t)
2.9b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
6.6b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_14589`
20×	`frac-sub_binary64_14577`
19×	`*-un-lft-identity_binary64_14568`
17×	`add-cube-cbrt_binary64_14600`
13×	`add-cbrt-cube_binary64_14601` `add-exp-log_binary64_14603`
12×	`times-frac_binary64_14574`
9×	`flip3--_binary64_14572` `flip--_binary64_14543`
8×	`frac-times_binary64_14578` `associate-*r/_binary64_14512`
7×	`associate-r_binary64_14510`
6×	`pow1_binary64_14626` `add-log-exp_binary64_14604` `associate-/r*_binary64_14514`
5×	`flip3-+_binary64_14571` `flip-+_binary64_14542` `sqrt-prod_binary64_14583`
4×	`associate-/l*_binary64_14515` `sqrt-div_binary64_14584` `associate--r+_binary64_14506`
3×	`div-exp_binary64_14616` `associate-l_binary64_14511` `sub-neg_binary64_14561` `cbrt-undiv_binary64_14599`
2×	`distribute-lft-in_binary64_14519` `associate-/l/_binary64_14517` `frac-2neg_binary64_14579` `clear-num_binary64_14567` `div-inv_binary64_14565` `cbrt-unprod_binary64_14598` `prod-exp_binary64_14614` `associate--l+_binary64_14507` `associate-*l/_binary64_14513` `distribute-rgt-in_binary64_14520` `unswap-sqr_binary64_14536`
1×	`diff-log_binary64_14657` `*-commutative_binary64_14501` `pow-prod-down_binary64_14636` `distribute-lft-out_binary64_14521`

Counts

4 → 104

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
9.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
3.0ms	(/.f64 2/3 t)

series609.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

362.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
128.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
101.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
19.0ms	(/.f64 2/3 t)

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4954	2992
1	4954	2992

prune209.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	4	117

Merged error: 0.7b

Counts

117 → 4

Compiler

Compiled 4727 to 2370 computations (49.9% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 2/3 t)
3.7b	(log.f64 (exp.f64 (/.f64 2/3 t)))
3.8b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
6.6b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_14589` `add-cube-cbrt_binary64_14600` `*-un-lft-identity_binary64_14568`
21×	`times-frac_binary64_14574`
14×	`log-pow_binary64_14654`
13×	`exp-prod_binary64_14617`
11×	`add-cbrt-cube_binary64_14601` `add-exp-log_binary64_14603`
8×	`frac-sub_binary64_14577`
7×	`flip3--_binary64_14572` `flip--_binary64_14543`
6×	`add-log-exp_binary64_14604` `associate-/r*_binary64_14514`
5×	`pow1_binary64_14626`
4×	`associate-/l_binary64_14515` `frac-times_binary64_14578` `associate--r+_binary64_14506` `associate-r/_binary64_14512`
3×	`div-exp_binary64_14616` `div-inv_binary64_14565` `log-prod_binary64_14651` `sub-neg_binary64_14561` `cbrt-undiv_binary64_14599`
2×	`distribute-lft-in_binary64_14519` `associate-/l/_binary64_14517` `frac-2neg_binary64_14579` `clear-num_binary64_14567` `associate--l+_binary64_14507` `associate-*l/_binary64_14513` `sqrt-div_binary64_14584` `distribute-rgt-in_binary64_14520`
1×	`flip3-+_binary64_14571` `diff-log_binary64_14657` `cbrt-unprod_binary64_14598` `prod-exp_binary64_14614` `rem-log-exp_binary64_14606` `flip-+_binary64_14542`

Counts

4 → 98

Calls

4 calls:

14.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
5.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
3.0ms	(/.f64 2/3 t)

series754.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

473.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
135.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
121.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
25.0ms	(/.f64 2/3 t)

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4968	2291
1	4968	2291

prune175.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	110	4	114

Merged error: 0.7b

Counts

114 → 4

Compiler

Compiled 4374 to 2268 computations (48.1% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.4b	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c))
5.5b	(.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))
7.8b	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c)))))
21.0b	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))) (*.f64 t (+.f64 b c)))

rewrite242.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

506×	`associate-*r/_binary64_14512`
326×	`frac-sub_binary64_14577`
252×	`frac-times_binary64_14578`
226×	`flip3-+_binary64_14571` `flip-+_binary64_14542`
174×	`sqrt-div_binary64_14584`
138×	`flip3--_binary64_14572` `flip--_binary64_14543`
126×	`associate-*l/_binary64_14513`
114×	`associate-/l/_binary64_14517`
19×	`add-cbrt-cube_binary64_14601` `add-exp-log_binary64_14603`
14×	`pow1_binary64_14626`
10×	`distribute-lft-in_binary64_14519` `distribute-rgt-in_binary64_14520` `*-un-lft-identity_binary64_14568`
9×	`sub-neg_binary64_14561`
8×	`add-sqr-sqrt_binary64_14589` `add-cube-cbrt_binary64_14600`
7×	`cbrt-unprod_binary64_14598` `prod-exp_binary64_14614`
6×	`pow-prod-down_binary64_14636` `add-log-exp_binary64_14604`
5×	`associate-r_binary64_14510`
4×	`associate-l_binary64_14511` `associate--r+_binary64_14506`
3×	`associate-/l*_binary64_14515` `times-frac_binary64_14574`
2×	`associate-/r/_binary64_14516` `div-exp_binary64_14616` `*-commutative_binary64_14501` `associate--l+_binary64_14507` `cbrt-undiv_binary64_14599`
1×	`diff-log_binary64_14657` `frac-2neg_binary64_14579` `clear-num_binary64_14567` `div-inv_binary64_14565` `div-sub_binary64_14573` `associate-/r*_binary64_14514` `distribute-lft-out_binary64_14521`

Counts

4 → 332

Calls

4 calls:

42.0ms	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))) (*.f64 t (+.f64 b c)))
27.0ms	(.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))
26.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c)))))
13.0ms	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c))

series3.0s (17.6%)

Counts

4 → 12

Calls

4 calls:

1.5s	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))) (*.f64 t (+.f64 b c)))
1.0s	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c)))))
252.0ms	(.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))
236.0ms	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c))

simplify235.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5086	26854

prune1.6s (9.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	342	2	344
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	343	5	348

Merged error: 0b

Counts

348 → 5

Compiler

Compiled 33691 to 13688 computations (59.4% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (.f64 b b) (.f64 c c))
3.4b	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c))
7.8b	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 (.f64 t (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))) (-.f64 (.f64 b b) (.f64 c c))))
21.0b	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 (.f64 t (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))) (-.f64 (.f64 b b) (.f64 c c)))) (*.f64 t (+.f64 b c)))

rewrite216.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

458×	`associate-*r/_binary64_14512`
320×	`frac-sub_binary64_14577`
244×	`frac-times_binary64_14578`
223×	`flip3-+_binary64_14571` `flip-+_binary64_14542`
174×	`sqrt-div_binary64_14584`
131×	`flip3--_binary64_14572` `flip--_binary64_14543`
122×	`associate-*l/_binary64_14513`
114×	`associate-/l/_binary64_14517`
14×	`add-cbrt-cube_binary64_14601` `add-exp-log_binary64_14603`
9×	`pow1_binary64_14626` `*-un-lft-identity_binary64_14568`
8×	`add-log-exp_binary64_14604`
7×	`add-sqr-sqrt_binary64_14589` `add-cube-cbrt_binary64_14600`
4×	`associate-r_binary64_14510` `cbrt-unprod_binary64_14598` `prod-exp_binary64_14614` `sub-neg_binary64_14561`
3×	`associate-/l*_binary64_14515` `distribute-lft-in_binary64_14519` `distribute-rgt-in_binary64_14520` `pow-prod-down_binary64_14636` `times-frac_binary64_14574`
2×	`associate-/r/_binary64_14516` `div-exp_binary64_14616` `diff-log_binary64_14657` `associate--l+_binary64_14507` `associate--r+_binary64_14506` `cbrt-undiv_binary64_14599`
1×	`associate-l_binary64_14511` `difference-of-squares_binary64_14537` `frac-2neg_binary64_14579` `clear-num_binary64_14567` `div-inv_binary64_14565` `-commutative_binary64_14501` `div-sub_binary64_14573` `associate-/r_binary64_14514` `distribute-lft-out_binary64_14521`

Counts

4 → 306

Calls

4 calls:

39.0ms	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 (.f64 t (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))) (-.f64 (.f64 b b) (.f64 c c)))) (*.f64 t (+.f64 b c)))
28.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 (.f64 t (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))) (-.f64 (.f64 b b) (.f64 c c))))
14.0ms	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c))
4.0ms	(-.f64 (.f64 b b) (.f64 c c))

series2.8s (16.2%)

Counts

4 → 12

Calls

4 calls:

1.5s	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 (.f64 t (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))) (-.f64 (.f64 b b) (.f64 c c)))) (*.f64 t (+.f64 b c)))
1.0s	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 (.f64 t (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))) (-.f64 (.f64 b b) (.f64 c c))))
232.0ms	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c))
42.0ms	(-.f64 (.f64 b b) (.f64 c c))

simplify219.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

318 → 318

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5062	25750

prune1.5s (9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	318	0	318
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	318	5	323

Merged error: 0b

Counts

323 → 5

Compiler

Compiled 31879 to 12879 computations (59.6% saved)

regimes243.0ms (1.4%)

Compiler: Compiled 1650 to 1421 computations (13.9% saved)

bsearch374.0ms (2.2%)

Steps

Iters	Range		Point
8	5.307699439423771	83211.98056573598	5.416627480041501
10	9.804554622682771e-49	1.729975500131323e-34	6.201719403044977e-40
9	4.701353291302201e-113	1.3345126110181775e-105	4.992983829650677e-110
8	2.053914602915812e-262	1.3517705033630237e-258	9.758239268123568e-262
11	-5.4409313712749874e-42	-2.763423925772879e-74	-1.0658168667306906e-60

Compiler

Compiled 1 to 7 computations (-600% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	1046	402
1	1046	402

end0.0ms (0%)

sample2.3s (13.2%)

Algorithm

1×

intervals

Results

825.0ms	8000×	body	128	valid
512.0ms	4984×	body	128	nan

Compiler

Compiled 611 to 421 computations (31.1% saved)

Details

analyze2.0s (11.7%)

sample71.0ms (0.4%)

simplify197.0ms (1.1%)

prune5.0ms (0%)

localize29.0ms (0.2%)

rewrite51.0ms (0.3%)

series609.0ms (3.5%)

simplify60.0ms (0.3%)

prune209.0ms (1.2%)

localize26.0ms (0.2%)

rewrite48.0ms (0.3%)

series754.0ms (4.4%)

simplify69.0ms (0.4%)

prune175.0ms (1%)

localize36.0ms (0.2%)

rewrite242.0ms (1.4%)

series3.0s (17.6%)

simplify235.0ms (1.4%)

prune1.6s (9.5%)

localize31.0ms (0.2%)

rewrite216.0ms (1.3%)

series2.8s (16.2%)

simplify219.0ms (1.3%)

prune1.5s (9%)

regimes243.0ms (1.4%)

bsearch374.0ms (2.2%)

simplify41.0ms (0.2%)

end0.0ms (0%)

sample2.3s (13.2%)

Profiling