Details

analyze618.0ms (11.2%)

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
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)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	178×	body	128	valid
7.0ms	31×	body	2048	valid
4.0ms	21×	body	1024	valid
2.0ms	14×	body	512	valid
2.0ms	7×	body	4096	valid
1.0ms	25×	body	128	nan
0.0ms	5×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify193.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	309	18
1	309	18

prune8.0ms (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

Merged error: 32.1b

Counts

2 → 1

Compiler

Compiled 50 to 38 computations (24% saved)

localize19.0ms (0.3%)

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)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.1b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `times-frac_binary64`
10×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_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` `+-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series498.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

195.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
127.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
122.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
53.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify110.0ms (2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4828	1903
1	4828	1903

prune380.0ms (6.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 6.3b

Counts

93 → 9

Compiler

Compiled 7219 to 3701 computations (48.7% saved)

localize11.0ms (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))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.1b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64`
7×	`pow1_binary64`
5×	`associate-l_binary64`
4×	`distribute-lft-out_binary64` `prod-exp_binary64`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `1-exp_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-+l-_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

19.0ms	(.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
13.0ms	(+.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)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series477.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

195.0ms	(.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
124.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
105.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
53.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5234	1841

prune102.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	95	10	105

Merged error: 6.3b

Counts

105 → 10

Compiler

Compiled 2352 to 830 computations (64.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `cancel-sign-sub-inv_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 64

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series451.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
118.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
108.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
103.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4804	1342
1	4804	1342

prune75.0ms (1.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	76	10	86

Merged error: 6.3b

Counts

86 → 10

Compiler

Compiled 2445 to 433 computations (82.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 a)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64` `sqrt-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64` `cbrt-prod_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 55

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
1.0ms	(cbrt.f64 a)

series443.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt.f64 a)
117.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
106.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
55.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4914	970
1	4914	970

prune66.0ms (1.2%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	66	11	77

Merged error: 6.3b

Counts

77 → 11

Compiler

Compiled 1786 to 436 computations (75.6% saved)

regimes210.0ms (3.8%)

Compiler: Compiled 720 to 522 computations (27.5% saved)

bsearch132.0ms (2.4%)

Steps

Iters	Range		Point
8	4.575371571350041e+103	3.5137682369026495e+107	1.8362622646806402e+105
8	5.722386305116561e-124	2.18206064524191e-119	5.835011607741609e-124
7	2.122143227960374e-142	1.5096449843192667e-140	1.4844516945955604e-140
11	-2.9568430544839144e+171	-2.6830436756501767e+147	-9.156580055033079e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	118	93
1	118	93

end0.0ms (0%)

sample1.3s (23.5%)

Algorithm

1×

intervals

Results

264.0ms	1178×	body	2048	valid
241.0ms	5138×	body	128	valid
118.0ms	704×	body	1024	valid
113.0ms	430×	body	4096	valid
51.0ms	365×	body	512	valid
35.0ms	796×	body	128	nan
16.0ms	185×	body	256	valid
11.0ms	236×	body	128	invalid

Compiler

Compiled 248 to 170 computations (31.5% saved)

Details

analyze618.0ms (11.2%)

sample39.0ms (0.7%)

simplify193.0ms (3.5%)

prune8.0ms (0.1%)

localize19.0ms (0.3%)

rewrite43.0ms (0.8%)

series498.0ms (9.1%)

simplify110.0ms (2%)

prune380.0ms (6.9%)

localize11.0ms (0.2%)

rewrite50.0ms (0.9%)

series477.0ms (8.7%)

simplify56.0ms (1%)

prune102.0ms (1.9%)

localize11.0ms (0.2%)

rewrite35.0ms (0.6%)

series451.0ms (8.2%)

simplify70.0ms (1.3%)

prune75.0ms (1.4%)

localize12.0ms (0.2%)

rewrite27.0ms (0.5%)

series443.0ms (8.1%)

simplify61.0ms (1.1%)

prune66.0ms (1.2%)

regimes210.0ms (3.8%)

bsearch132.0ms (2.4%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.3s (23.5%)

Profiling