Details

analyze611.0ms (10.8%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	188×	body	128	valid
6.0ms	27×	body	2048	valid
3.0ms	20×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	23×	body	128	nan
1.0ms	6×	body	256	valid
1.0ms	4×	body	512	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify190.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	309	20
1	309	20

prune4.0ms (0.1%)

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: 31.8b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
11×	`sqrt-prod_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 96

Calls

4 calls:

17.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
13.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series436.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
118.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
117.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
51.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4935	2578
1	4935	2578

prune376.0ms (6.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	11	109

Merged error: 4.9b

Counts

109 → 11

Compiler

Compiled 7756 to 3546 computations (54.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64`
8×	`sqrt-prod_binary64`
7×	`pow1_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`diff-log_binary64` `unswap-sqr_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate--l-_binary64` `1-exp_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

18.0ms	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series442.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

157.0ms	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
114.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
57.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5299	2204

prune128.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	106	11	117

Merged error: 4.9b

Counts

117 → 11

Compiler

Compiled 2995 to 1063 computations (64.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite62.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
132×	`add-sqr-sqrt_binary64`
131×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
19×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 182

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
11.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series480.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

196.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
120.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
111.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
53.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4998	5933
1	4998	5933

prune178.0ms (3.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	194	11	205

Merged error: 4.8b

Counts

205 → 11

Compiler

Compiled 5221 to 1114 computations (78.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0b	(-.f64 (neg.f64 b_2) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
24.5b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
24.5b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`diff-log_binary64`
2×	`sub-neg_binary64` `pow1/3_binary64` `cancel-sign-sub-inv_binary64`
1×	`associate--l-_binary64` `neg-sub0_binary64` `neg-log_binary64`

Counts

4 → 52

Calls

4 calls:

5.0ms	(-.f64 (neg.f64 b_2) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series573.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(-.f64 (neg.f64 b_2) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
158.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
154.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
49.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5237	1482

prune59.0ms (1.1%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	64	11	75

Merged error: 4.8b

Counts

75 → 11

Compiler

Compiled 1936 to 396 computations (79.5% saved)

regimes261.0ms (4.6%)

Compiler: Compiled 839 to 545 computations (35% saved)

bsearch68.0ms (1.2%)

Steps

Iters	Range		Point
10	2.6984454119678255e-12	3.813352894740704	3.7738771228718737
9	-1.2594274734414935e-50	-3.252894960030989e-60	-2.179096873024578e-55

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	111	55
1	111	55

end0.0ms (0%)

sample1.2s (22.1%)

Algorithm

1×

intervals

Results

249.0ms	1174×	body	2048	valid
242.0ms	5161×	body	128	valid
127.0ms	721×	body	1024	valid
99.0ms	358×	body	4096	valid
49.0ms	388×	body	512	valid
33.0ms	777×	body	128	nan
17.0ms	198×	body	256	valid
12.0ms	260×	body	128	invalid

Compiler

Compiled 232 to 155 computations (33.2% saved)

Details

analyze611.0ms (10.8%)

sample38.0ms (0.7%)

simplify190.0ms (3.4%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite53.0ms (0.9%)

series436.0ms (7.7%)

simplify88.0ms (1.6%)

prune376.0ms (6.7%)

localize10.0ms (0.2%)

rewrite47.0ms (0.8%)

series442.0ms (7.8%)

simplify63.0ms (1.1%)

prune128.0ms (2.3%)

localize11.0ms (0.2%)

rewrite62.0ms (1.1%)

series480.0ms (8.5%)

simplify100.0ms (1.8%)

prune178.0ms (3.2%)

localize16.0ms (0.3%)

rewrite24.0ms (0.4%)

series573.0ms (10.2%)

simplify56.0ms (1%)

prune59.0ms (1.1%)

regimes261.0ms (4.6%)

bsearch68.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (22.1%)

Profiling