Details

analyze898.0ms (19%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
33.3%	66.5%	0.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	27×	body	128	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify224.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4989	16
1	4989	16

prune2.0ms (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

1.7b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
2.6b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

rewrite41.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64_15786`
71×	`*-un-lft-identity_binary64_15764`
51×	`times-frac_binary64_15770`
31×	`associate-r_binary64_15704`
27×	`add-cube-cbrt_binary64_15799`
22×	`distribute-lft-out--_binary64_15716` `difference-of-squares_binary64_15733`
10×	`add-cbrt-cube_binary64_15800` `add-exp-log_binary64_15802`
5×	`add-log-exp_binary64_15803` `associate-/r_binary64_15708` `associate-/l_binary64_15709` `pow1_binary64_15825`
4×	`associate-/r/_binary64_15710`
3×	`associate-l_binary64_15705` `flip--_binary64_15739` `flip3--_binary64_15768`
2×	`cbrt-undiv_binary64_15798` `div-inv_binary64_15761` `cbrt-unprod_binary64_15797` `prod-exp_binary64_15813` `associate-/l/_binary64_15711` `unswap-sqr_binary64_15732` `div-exp_binary64_15815`
1×	`flip3-+_binary64_15767` `associate-r/_binary64_15706` `sum-log_binary64_15855` `frac-2neg_binary64_15775` `clear-num_binary64_15763` `-commutative_binary64_15695` `div-sub_binary64_15769` `+-commutative_binary64_15694` `flip-+_binary64_15738` `pow-prod-down_binary64_15835`

Counts

3 → 113

Calls

3 calls:

20.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
8.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
3.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

series218.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

113.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
71.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
34.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5134	2068

prune100.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	7	123

Error

0.0b

Counts

123 → 7

Compiler

Compiled 2341 to 516 computations (78% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))))
0.0b	(/.f64 1 (-.f64 z a))
0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
2.6b	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))))

rewrite52.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_15786`
42×	`*-un-lft-identity_binary64_15764`
32×	`add-exp-log_binary64_15802` `times-frac_binary64_15770`
25×	`add-cube-cbrt_binary64_15799`
22×	`associate-r_binary64_15704`
20×	`add-cbrt-cube_binary64_15800`
13×	`prod-exp_binary64_15813`
12×	`pow1_binary64_15825`
8×	`distribute-lft-out--_binary64_15716` `associate-r/_binary64_15706` `difference-of-squares_binary64_15733` `associate-l*_binary64_15705`
7×	`cbrt-unprod_binary64_15797`
6×	`add-log-exp_binary64_15803` `flip--_binary64_15739` `flip3--_binary64_15768` `div-exp_binary64_15815`
5×	`associate-/r*_binary64_15708`
4×	`associate-*l/_binary64_15707` `frac-times_binary64_15774` `pow-prod-down_binary64_15835` `associate-/r/_binary64_15710`
3×	`cbrt-undiv_binary64_15798` `unswap-sqr_binary64_15732` `rec-exp_binary64_15814` `associate-/l*_binary64_15709` `1-exp_binary64_15808`
2×	`div-inv_binary64_15761` `un-div-inv_binary64_15762` `*-commutative_binary64_15695`
1×	`flip3-+_binary64_15767` `inv-pow_binary64_15849` `sum-log_binary64_15855` `pow-flip_binary64_15838` `frac-2neg_binary64_15775` `clear-num_binary64_15763` `+-commutative_binary64_15694` `flip-+_binary64_15738`

Counts

4 → 130

Calls

4 calls:

15.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
13.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))))
6.0ms	(/.f64 1 (-.f64 z a))
4.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))))

series241.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))))
70.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))))
34.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
19.0ms	(/.f64 1 (-.f64 z a))

simplify63.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5131	1919

prune104.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	142	7	149

Error

0.0b

Counts

149 → 7

Compiler

Compiled 2545 to 877 computations (65.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 z a))
0.5b	(cbrt.f64 (-.f64 z a))
0.6b	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
8.0b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))

rewrite81.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-sqr-sqrt_binary64_15786`
79×	`*-un-lft-identity_binary64_15764`
65×	`cbrt-prod_binary64_15795`
54×	`associate-r_binary64_15704`
50×	`times-frac_binary64_15770`
35×	`add-cube-cbrt_binary64_15799`
30×	`cbrt-div_binary64_15796`
27×	`add-exp-log_binary64_15802`
23×	`associate-l_binary64_15705`
21×	`distribute-lft-out--_binary64_15716`
19×	`difference-of-squares_binary64_15733`
18×	`add-cbrt-cube_binary64_15800`
15×	`flip--_binary64_15739` `flip3--_binary64_15768`
13×	`pow1_binary64_15825`
10×	`swap-sqr_binary64_15731` `unswap-sqr_binary64_15732` `associate-/r/_binary64_15710`
9×	`cbrt-unprod_binary64_15797` `frac-times_binary64_15774` `prod-exp_binary64_15813`
8×	`pow1/3_binary64_15846`
7×	`cbrt-undiv_binary64_15798` `div-exp_binary64_15815`
5×	`associate-l/_binary64_15707` `associate-r/_binary64_15706`
4×	`add-log-exp_binary64_15803`
3×	`pow-prod-down_binary64_15835`
2×	`pow-sqr_binary64_15737` `div-inv_binary64_15761` `*-commutative_binary64_15695` `pow-prod-up_binary64_15834`
1×	`pow2_binary64_15845` `pow-plus_binary64_15827`

Counts

4 → 177

Calls

4 calls:

42.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))
12.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
3.0ms	(cbrt.f64 (-.f64 z a))
3.0ms	(cbrt.f64 (-.f64 z a))

series476.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))
117.0ms	(cbrt.f64 (-.f64 z a))
115.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
113.0ms	(cbrt.f64 (-.f64 z a))

simplify91.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4959	3968
1	4959	3968

prune178.0ms (3.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	188	8	196

Error

Counts

196 → 8

Compiler

Compiled 5325 to 1346 computations (74.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (pow.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 z a))) 1))
10.5b	(*.f64 (-.f64 z t) (/.f64 y (-.f64 z a)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_15786`
22×	`*-un-lft-identity_binary64_15764`
21×	`associate-r_binary64_15704`
16×	`times-frac_binary64_15770`
12×	`add-cube-cbrt_binary64_15799`
7×	`add-cbrt-cube_binary64_15800` `add-exp-log_binary64_15802`
5×	`associate-l_binary64_15705`
4×	`add-log-exp_binary64_15803` `distribute-lft-out--_binary64_15716` `difference-of-squares_binary64_15733` `pow1_binary64_15825`
3×	`flip--_binary64_15739` `flip3--_binary64_15768`
2×	`associate-*l/_binary64_15707` `cbrt-unprod_binary64_15797` `frac-times_binary64_15774` `prod-exp_binary64_15813` `unswap-sqr_binary64_15732` `associate-/r/_binary64_15710`
1×	`cbrt-undiv_binary64_15798` `flip3-+_binary64_15767` `associate-r/_binary64_15706` `distribute-lft-out_binary64_15715` `sum-log_binary64_15855` `div-inv_binary64_15761` `-commutative_binary64_15695` `+-commutative_binary64_15694` `flip-+_binary64_15738` `pow-prod-down_binary64_15835` `div-exp_binary64_15815`

Counts

2 → 58

Calls

2 calls:

14.0ms	(*.f64 (-.f64 z t) (/.f64 y (-.f64 z a)))
4.0ms	(+.f64 x (pow.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 z a))) 1))

series155.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

100.0ms	(+.f64 x (pow.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 z a))) 1))
55.0ms	(*.f64 (-.f64 z t) (/.f64 y (-.f64 z a)))

simplify52.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5000	1078

prune51.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	65	7	72

Error

Counts

72 → 7

Compiler

Compiled 1214 to 358 computations (70.5% saved)

regimes439.0ms (9.3%)

Accuracy

Total 1.4b remaining (99.8%)

Threshold costs 0b (0%)

Compiler

Compiled 3937 to 2933 computations (25.5% saved)

bsearch39.0ms (0.8%)

Steps

Iters	Range		Point
10	2.040786514124688e-244	9.055313654549201e-234	2.5724907750237608e-244
4	-6.239455203090877e-179	-4.333293522143732e-179	-5.7951150117792e-179

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	49
1	49	49

end0.0ms (0%)

sample1.1s (22.7%)

Algorithm

1×

intervals

Results

313.0ms	8000×	body	128	valid
30.0ms	705×	body	128	invalid

Compiler

Compiled 526 to 389 computations (26% saved)

Details

analyze898.0ms (19%)

sample25.0ms (0.5%)

simplify224.0ms (4.7%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite41.0ms (0.9%)

series218.0ms (4.6%)

simplify65.0ms (1.4%)

prune100.0ms (2.1%)

localize10.0ms (0.2%)

rewrite52.0ms (1.1%)

series241.0ms (5.1%)

simplify63.0ms (1.3%)

prune104.0ms (2.2%)

localize13.0ms (0.3%)

rewrite81.0ms (1.7%)

series476.0ms (10.1%)

simplify91.0ms (1.9%)

prune178.0ms (3.7%)

localize9.0ms (0.2%)

rewrite23.0ms (0.5%)

series155.0ms (3.3%)

simplify52.0ms (1.1%)

prune51.0ms (1.1%)

regimes439.0ms (9.3%)

bsearch39.0ms (0.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (22.7%)

Profiling