Details

analyze761.0ms (7.2%)

Algorithm

1×

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
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample57.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	174×	body	128	valid
8.0ms	32×	body	1024	valid
7.0ms	26×	body	1024	nan
6.0ms	29×	body	512	valid
4.0ms	23×	body	512	nan
3.0ms	47×	body	128	nan
3.0ms	21×	body	256	valid
1.0ms	8×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify227.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5009	41

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

Merged error: 43.3b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
14.3b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
20.6b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite71.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_101`
13×	`sqrt-prod_binary64_95`
12×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
11×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
7×	`pow1_binary64_140`
6×	`associate-/r_binary64_23` `associate-l*_binary64_20` `times-frac_binary64_85` `add-log-exp_binary64_118`
4×	`sqrt-div_binary64_96`
3×	`flip--_binary64_54` `flip3--_binary64_83` `associate-r_binary64_19`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `associate--l+_binary64_16` `unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `associate-/r/_binary64_25`
1×	`div-inv_binary64_76` `distribute-lft-in_binary64_28` `associate-/l_binary64_24` `rem-sqrt-square_binary64_92` `-commutative_binary64_10` `pow-prod-down_binary64_150` `sqrt-pow1_binary64_97` `diff-log_binary64_171` `clear-num_binary64_78` `pow1/2_binary64_159` `cancel-sign-sub-inv_binary64_45` `distribute-rgt-in_binary64_29` `sub-neg_binary64_72` `frac-2neg_binary64_90`

Counts

4 → 80

Calls

4 calls:

20.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
19.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
16.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
5.0ms	(*.f64 (sqrt.f64 2) t)

series2.8s (26.4%)

Counts

4 → 12

Calls

4 calls:

1.6s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
816.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
327.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
49.0ms	(*.f64 (sqrt.f64 2) t)

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4955	3058
1	4955	3058

prune925.0ms (8.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 6.7b

Counts

93 → 7

Compiler

Compiled 20553 to 13636 computations (33.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.7b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.7b	(/.f64 (*.f64 l l) x)
7.8b	(/.f64 (*.f64 t t) x)
26.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
10×	`add-sqr-sqrt_binary64_101`
9×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
8×	`associate-*r/_binary64_21`
6×	`associate-/r*_binary64_23` `times-frac_binary64_85` `add-log-exp_binary64_118`
5×	`pow1_binary64_140`
4×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `flip-+_binary64_53` `frac-add_binary64_87` `sqrt-div_binary64_96` `flip3-+_binary64_82`
3×	`sqrt-prod_binary64_95`
2×	`div-inv_binary64_76` `associate-/l*_binary64_24` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `associate-+r+_binary64_11` `clear-num_binary64_78` `frac-2neg_binary64_90`
1×	`sum-log_binary64_170` `distribute-lft-in_binary64_28` `+-commutative_binary64_9` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29`

Counts

4 → 74

Calls

4 calls:

9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)

series328.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

188.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
90.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
26.0ms	(/.f64 (*.f64 l l) x)
24.0ms	(/.f64 (*.f64 t t) x)

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5003	1976

prune540.0ms (5.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	80	13	93

Merged error: 5.2b

Counts

93 → 13

Compiler

Compiled 12791 to 7618 computations (40.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
4.7b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
7.8b	(/.f64 (*.f64 t t) x)
26.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-sqr-sqrt_binary64_101` `associate-*r/_binary64_21` `add-log-exp_binary64_118`
7×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
5×	`flip-+_binary64_53` `flip3-+_binary64_82` `pow1_binary64_140`
4×	`frac-add_binary64_87` `sqrt-div_binary64_96`
3×	`sqrt-prod_binary64_95` `associate-/r*_binary64_23` `times-frac_binary64_85`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `sum-log_binary64_170` `+-commutative_binary64_9` `associate-+r+_binary64_11`
1×	`div-inv_binary64_76` `distribute-lft-in_binary64_28` `associate-/l*_binary64_24` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

Counts

4 → 64

Calls

4 calls:

14.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
6.0ms	(/.f64 (*.f64 t t) x)

series351.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
87.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
54.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
26.0ms	(/.f64 (*.f64 t t) x)

simplify45.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5206	2011

prune234.0ms (2.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	75	14	89

Merged error: 5.2b

Counts

89 → 14

Compiler

Compiled 5736 to 3116 computations (45.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.8b	(/.f64 (*.f64 t t) x)
26.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))) (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))))
27.2b	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))
27.2b	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))

rewrite54.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-div_binary64_96`
18×	`associate-*r/_binary64_21`
12×	`add-sqr-sqrt_binary64_101`
9×	`sqrt-prod_binary64_95` `add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `flip-+_binary64_53` `add-cube-cbrt_binary64_114` `flip3-+_binary64_82` `*-un-lft-identity_binary64_79`
8×	`frac-add_binary64_87`
7×	`pow1_binary64_140`
4×	`frac-times_binary64_89` `add-log-exp_binary64_118`
3×	`associate-/r*_binary64_23` `times-frac_binary64_85` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `associate-*l/_binary64_22`
1×	`div-inv_binary64_76` `associate-/l*_binary64_24` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `clear-num_binary64_78` `frac-2neg_binary64_90`

Counts

4 → 74

Calls

4 calls:

13.0ms	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))
13.0ms	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))
11.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))) (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))))
5.0ms	(/.f64 (*.f64 t t) x)

series410.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))) (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))))
105.0ms	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))
98.0ms	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))
24.0ms	(/.f64 (*.f64 t t) x)

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4946	2424
1	4946	2424

prune281.0ms (2.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	86	14	100

Merged error: 5.2b

Counts

100 → 14

Compiler

Compiled 7415 to 3491 computations (52.9% saved)

regimes513.0ms (4.8%)

Compiler: Compiled 4055 to 2541 computations (37.3% saved)

bsearch375.0ms (3.5%)

Steps

Iters	Range		Point
7	1.9128883414062255e+139	3.7912004233333035e+140	8.156962978641518e+139
9	7.340996980453347e-157	1.6707997971669048e-150	7.461103816305763e-157
10	8.129140683311145e-213	8.406421684544448e-203	8.323497236838193e-203
8	-2.2070269993913444e+112	-1.1016096422962694e+108	-7.022737789257463e+109

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	157	166
1	157	166

end0.0ms (0%)

sample2.3s (21.4%)

Algorithm

1×

intervals

Results

376.0ms	5333×	body	128	valid
312.0ms	1158×	body	1024	valid
235.0ms	873×	body	1024	nan
178.0ms	889×	body	512	valid
105.0ms	532×	body	512	nan
104.0ms	1536×	body	128	nan
78.0ms	550×	body	256	valid
35.0ms	273×	body	256	nan
24.0ms	70×	body	2048	valid

Compiler

Compiled 807 to 503 computations (37.7% saved)

Details

analyze761.0ms (7.2%)

sample57.0ms (0.5%)

simplify227.0ms (2.1%)

prune3.0ms (0%)

localize16.0ms (0.2%)

rewrite71.0ms (0.7%)

series2.8s (26.4%)

simplify73.0ms (0.7%)

prune925.0ms (8.7%)

localize16.0ms (0.1%)

rewrite36.0ms (0.3%)

series328.0ms (3.1%)

simplify63.0ms (0.6%)

prune540.0ms (5.1%)

localize19.0ms (0.2%)

rewrite46.0ms (0.4%)

series351.0ms (3.3%)

simplify45.0ms (0.4%)

prune234.0ms (2.2%)

localize19.0ms (0.2%)

rewrite54.0ms (0.5%)

series410.0ms (3.9%)

simplify81.0ms (0.8%)

prune281.0ms (2.6%)

regimes513.0ms (4.8%)

bsearch375.0ms (3.5%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.3s (21.4%)

Profiling