Details

analyze1.0s (11.6%)

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
3.1%	96.7%	0.2%	8
19.9%	79.9%	0.2%	9
22.8%	77%	0.2%	10
35.1%	64.7%	0.2%	11
45%	54.8%	0.2%	12
53.8%	45.1%	1.2%	13
56.2%	42.4%	1.5%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample32.0ms (0.4%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	17×	body	128	invalid

Compiler

Compiled 19 to 21 computations (-10.5% saved)

simplify658.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (491.0ms)

Iter	Nodes	Cost
0	5412	13

prune4.0ms (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: 1.9b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
1.9b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

rewrite61.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64_11694`
70×	`*-un-lft-identity_binary64_11672`
51×	`times-frac_binary64_11678`
31×	`associate-l_binary64_11613`
26×	`add-cube-cbrt_binary64_11707`
22×	`distribute-lft-out--_binary64_11624` `difference-of-squares_binary64_11641`
9×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
5×	`associate-/r_binary64_11616` `associate-/l_binary64_11617`
4×	`associate-/r/_binary64_11618` `pow1_binary64_11733`
3×	`associate-r_binary64_11612` `flip3--_binary64_11676` `flip--_binary64_11647`
2×	`cbrt-undiv_binary64_11706` `cbrt-unprod_binary64_11705` `div-exp_binary64_11723` `add-log-exp_binary64_11711` `unswap-sqr_binary64_11640` `prod-exp_binary64_11721` `div-inv_binary64_11669` `associate-/l/_binary64_11619`
1×	`clear-num_binary64_11671` `associate-l/_binary64_11615` `div-sub_binary64_11677` `frac-2neg_binary64_11683` `-commutative_binary64_11603` `pow-prod-down_binary64_11743`

Counts

2 → 102

Calls

2 calls:

27.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
17.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

series289.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

209.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
80.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify117.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5037	1792

prune159.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	8	109

Merged error: 0b

Counts

109 → 8

Compiler

Compiled 1901 to 429 computations (77.4% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 x y))
0.6b	(cbrt.f64 (-.f64 x y))
0.7b	(*.f64 t (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)))
6.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 t (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y))))

rewrite130.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64_11694` `add-exp-log_binary64_11710`
58×	`*-un-lft-identity_binary64_11672`
47×	`associate-r_binary64_11612`
45×	`times-frac_binary64_11678`
36×	`cbrt-prod_binary64_11703`
35×	`add-cbrt-cube_binary64_11708`
33×	`prod-exp_binary64_11721`
28×	`add-cube-cbrt_binary64_11707`
20×	`cbrt-unprod_binary64_11705`
18×	`div-exp_binary64_11723`
15×	`distribute-lft-out--_binary64_11624` `difference-of-squares_binary64_11641`
11×	`pow1_binary64_11733`
10×	`cbrt-undiv_binary64_11706` `associate-l_binary64_11613`
6×	`1-exp_binary64_11716`
4×	`add-log-exp_binary64_11711` `associate-*r/_binary64_11614` `cbrt-div_binary64_11704` `pow-prod-down_binary64_11743`
3×	`flip3--_binary64_11676` `unswap-sqr_binary64_11640` `flip--_binary64_11647`
2×	`associate-/r/_binary64_11618` `pow1/3_binary64_11754` `div-inv_binary64_11669` `*-commutative_binary64_11603`
1×	`frac-times_binary64_11682` `associate-*l/_binary64_11615`

Counts

4 → 141

Calls

4 calls:

44.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 t (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y))))
37.0ms	(*.f64 t (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)))
6.0ms	(cbrt.f64 (-.f64 x y))
6.0ms	(cbrt.f64 (-.f64 x y))

series900.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

356.0ms	(*.f64 t (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)))
207.0ms	(cbrt.f64 (-.f64 x y))
199.0ms	(cbrt.f64 (-.f64 x y))
137.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 t (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y))))

simplify163.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4961	2424
1	4961	2424

prune223.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	153	8	161

Merged error: 0b

Counts

161 → 8

Compiler

Compiled 3922 to 866 computations (77.9% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 z y))
0.5b	(*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))
0.6b	(*.f64 t (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 z y))))
6.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (*.f64 t (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 z y)))))

rewrite171.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-exp-log_binary64_11710`
87×	`add-sqr-sqrt_binary64_11694`
77×	`*-un-lft-identity_binary64_11672`
59×	`cbrt-prod_binary64_11703`
55×	`associate-r_binary64_11612`
47×	`prod-exp_binary64_11721`
45×	`times-frac_binary64_11678`
35×	`add-cube-cbrt_binary64_11707` `add-cbrt-cube_binary64_11708`
28×	`cbrt-div_binary64_11704`
26×	`associate-l_binary64_11613`
21×	`cbrt-unprod_binary64_11705`
20×	`distribute-lft-out--_binary64_11624` `div-exp_binary64_11723`
18×	`pow1_binary64_11733` `difference-of-squares_binary64_11641`
14×	`flip3--_binary64_11676` `flip--_binary64_11647`
10×	`cbrt-undiv_binary64_11706` `associate-/r/_binary64_11618` `swap-sqr_binary64_11639`
9×	`frac-times_binary64_11682`
8×	`associate-*r/_binary64_11614`
7×	`unswap-sqr_binary64_11640` `pow1/3_binary64_11754`
6×	`1-exp_binary64_11716` `pow-prod-down_binary64_11743` `rec-exp_binary64_11722`
5×	`associate-*l/_binary64_11615`
4×	`add-log-exp_binary64_11711`
3×	`*-commutative_binary64_11603`
2×	`pow-sqr_binary64_11645` `pow-prod-up_binary64_11742` `div-inv_binary64_11669`
1×	`pow2_binary64_11753` `pow-plus_binary64_11735`

Counts

4 → 196

Calls

4 calls:

53.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (*.f64 t (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 z y)))))
37.0ms	(*.f64 t (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 z y))))
23.0ms	(*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))
6.0ms	(cbrt.f64 (-.f64 z y))

series1.1s (12.5%)

Counts

4 → 12

Calls

4 calls:

368.0ms	(*.f64 t (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 z y))))
305.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (*.f64 t (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 z y)))))
227.0ms	(*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))
222.0ms	(cbrt.f64 (-.f64 z y))

simplify157.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4947	3634
1	4947	3634

prune341.0ms (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	209	7	216

Merged error: 0b

Counts

216 → 7

Compiler

Compiled 5446 to 1265 computations (76.8% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 z y) (-.f64 x y))
2.3b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

rewrite84.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64_11678`
194×	`add-sqr-sqrt_binary64_11694` `*-un-lft-identity_binary64_11672`
90×	`add-cube-cbrt_binary64_11707`
52×	`distribute-lft-out--_binary64_11624` `difference-of-squares_binary64_11641`
36×	`associate-/r*_binary64_11616`
11×	`associate-/r/_binary64_11618`
9×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
8×	`associate-/l*_binary64_11617`
6×	`flip3--_binary64_11676` `div-inv_binary64_11669` `flip--_binary64_11647`
4×	`cbrt-undiv_binary64_11706` `div-exp_binary64_11723`
2×	`pow1_binary64_11733` `clear-num_binary64_11671` `add-log-exp_binary64_11711` `frac-2neg_binary64_11683` `associate-/l/_binary64_11619`
1×	`div-sub_binary64_11677`

Counts

2 → 194

Calls

2 calls:

26.0ms	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
16.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

series333.0ms (3.7%)

Counts

2 → 6

Calls

2 calls:

262.0ms	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
71.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

simplify159.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5009	4887

prune274.0ms (3.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	200	7	207

Merged error: 0b

Counts

207 → 7

Compiler

Compiled 4241 to 919 computations (78.3% saved)

regimes632.0ms (7.1%)

Compiler: Compiled 2805 to 1918 computations (31.6% saved)

bsearch62.0ms (0.7%)

Steps

Iters	Range		Point
6	1.2501452209405669e-116	5.125053173799247e-116	2.795632804998043e-116
8	3.6548673330568913e-299	7.328087859941358e-296	5.704566056545378e-299

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	58
1	41	58

end0.0ms (0%)

sample1.8s (19.6%)

Algorithm

1×

intervals

Results

490.0ms	8000×	body	128	valid
33.0ms	565×	body	128	invalid

Compiler

Compiled 489 to 331 computations (32.3% saved)

Details

analyze1.0s (11.6%)

sample32.0ms (0.4%)

simplify658.0ms (7.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

rewrite61.0ms (0.7%)

series289.0ms (3.2%)

simplify117.0ms (1.3%)

prune159.0ms (1.8%)

localize24.0ms (0.3%)

rewrite130.0ms (1.5%)

series900.0ms (10.1%)

simplify163.0ms (1.8%)

prune223.0ms (2.5%)

localize28.0ms (0.3%)

rewrite171.0ms (1.9%)

series1.1s (12.5%)

simplify157.0ms (1.8%)

prune341.0ms (3.8%)

localize16.0ms (0.2%)

rewrite84.0ms (0.9%)

series333.0ms (3.7%)

simplify159.0ms (1.8%)

prune274.0ms (3.1%)

regimes632.0ms (7.1%)

bsearch62.0ms (0.7%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.8s (19.6%)

Profiling