Details

analyze100.0ms (2.3%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
56.2%	43.7%	0.1%	7
56.2%	43.7%	0.1%	8
76.5%	23.4%	0.1%	9
76.5%	23.4%	0.1%	10
87.8%	12.1%	0.1%	11
87.8%	12.1%	0.1%	12
93.8%	6.1%	0.1%	13
93.8%	6.1%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample14.0ms (0.3%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify314.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	4932	10
1	4932	10

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 30 to 28 computations (6.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_17279`
3×	`add-log-exp_binary64_17318`
2×	`distribute-lft-out_binary64_17230` `times-frac_binary64_17285`
1×	`flip-+_binary64_17253` `pow1_binary64_17340` `sum-log_binary64_17370` `frac-add_binary64_17287` `add-sqr-sqrt_binary64_17301` `add-exp-log_binary64_17317` `flip3-+_binary64_17282` `+-commutative_binary64_17209` `add-cube-cbrt_binary64_17314` `add-cbrt-cube_binary64_17315`

Counts

1 → 14

Calls

1 calls:

15.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

series37.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

37.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4850	239
1	4850	239

prune25.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	14	3	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	4	18

Merged error: 0.0b

Counts

18 → 4

Compiler

Compiled 380 to 310 computations (18.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
0.5b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite92.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64_17279`
43×	`cbrt-prod_binary64_17310`
33×	`cbrt-div_binary64_17311`
23×	`add-sqr-sqrt_binary64_17301`
16×	`distribute-lft-out_binary64_17230`
15×	`add-cube-cbrt_binary64_17314`
14×	`times-frac_binary64_17285`
11×	`flip-+_binary64_17253` `pow1_binary64_17340` `frac-add_binary64_17287` `flip3-+_binary64_17282`
10×	`swap-sqr_binary64_17246`
9×	`pow1/3_binary64_17361` `frac-times_binary64_17289`
8×	`associate-l_binary64_17220` `associate-r_binary64_17219`
6×	`add-exp-log_binary64_17317`
4×	`unswap-sqr_binary64_17247` `add-cbrt-cube_binary64_17315` `add-log-exp_binary64_17318`
3×	`associate-r/_binary64_17221` `associate-l/_binary64_17222`
2×	`pow-prod-down_binary64_17350` `pow-prod-up_binary64_17349` `pow-sqr_binary64_17252`
1×	`cbrt-unprod_binary64_17312` `pow-plus_binary64_17342` `prod-exp_binary64_17328` `*-commutative_binary64_17210` `pow2_binary64_17360`

Counts

4 → 111

Calls

4 calls:

34.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
16.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series737.0ms (17.2%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
191.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
173.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
167.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify109.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4898	2939
1	4898	2939

prune262.0ms (6.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	123	4	127

Merged error: 0b

Counts

127 → 4

Compiler

Compiled 4416 to 3486 computations (21.1% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.5b	(cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) 2))
0.6b	(cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

rewrite71.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`cbrt-prod_binary64_17310`
35×	`*-un-lft-identity_binary64_17279`
12×	`cbrt-div_binary64_17311`
11×	`add-sqr-sqrt_binary64_17301` `add-cube-cbrt_binary64_17314`
8×	`unpow-prod-down_binary64_17358` `distribute-lft-out_binary64_17230` `times-frac_binary64_17285`
4×	`pow1/3_binary64_17361` `pow1_binary64_17340` `add-exp-log_binary64_17317` `add-cbrt-cube_binary64_17315` `add-log-exp_binary64_17318`
3×	`flip-+_binary64_17253` `frac-add_binary64_17287` `flip3-+_binary64_17282`
1×	`sqr-pow_binary64_17251` `unpow2_binary64_17344`

Counts

4 → 72

Calls

4 calls:

17.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
16.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) 2))
14.0ms	(cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series737.0ms (17.2%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) 2))
190.0ms	(cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
179.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
167.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify99.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4779	1903
1	4779	1903

prune208.0ms (4.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	84	4	88

Merged error: 0b

Counts

88 → 4

Compiler

Compiled 3964 to 3175 computations (19.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1/4 (*.f64 x x))
0.5b	(/.f64 1/4 (*.f64 y y))
3.9b	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
31.6b	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite79.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

238×	`add-sqr-sqrt_binary64_17301`
194×	`times-frac_binary64_17285`
112×	`*-un-lft-identity_binary64_17279`
84×	`difference-of-squares_binary64_17248`
42×	`distribute-lft-out--_binary64_17231`
30×	`add-cube-cbrt_binary64_17314`
26×	`div-inv_binary64_17276`
16×	`add-exp-log_binary64_17317` `add-cbrt-cube_binary64_17315`
15×	`associate-/l*_binary64_17224`
11×	`associate-/r*_binary64_17223`
7×	`cancel-sign-sub-inv_binary64_17245`
6×	`add-log-exp_binary64_17318`
5×	`div-exp_binary64_17330` `cbrt-undiv_binary64_17313`
4×	`pow1_binary64_17340`
3×	`clear-num_binary64_17278` `flip3--_binary64_17283` `frac-2neg_binary64_17290` `frac-sub_binary64_17288` `flip--_binary64_17254` `associate-/l/_binary64_17226` `associate-/r/_binary64_17225`
2×	`cbrt-unprod_binary64_17312` `prod-exp_binary64_17328`
1×	`diff-log_binary64_17371` `div-sub_binary64_17284` `sub-neg_binary64_17272`

Counts

4 → 185

Calls

4 calls:

29.0ms	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
11.0ms	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
5.0ms	(/.f64 1/4 (*.f64 y y))
5.0ms	(/.f64 1/4 (*.f64 x x))

series228.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
48.0ms	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
44.0ms	(/.f64 1/4 (*.f64 y y))
33.0ms	(/.f64 1/4 (*.f64 x x))

simplify119.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4901	6441
1	4901	6441

prune340.0ms (7.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	196	5	201

Merged error: 0b

Counts

201 → 5

Compiler

Compiled 5931 to 3940 computations (33.6% saved)

regimes30.0ms (0.7%)

Compiler: Compiled 204 to 180 computations (11.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample539.0ms (12.6%)

Algorithm

1×

intervals

Results

241.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 124 to 110 computations (11.3% saved)

Details

analyze100.0ms (2.3%)

sample14.0ms (0.3%)

simplify314.0ms (7.3%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

rewrite16.0ms (0.4%)

series37.0ms (0.9%)

simplify84.0ms (1.9%)

prune25.0ms (0.6%)

localize9.0ms (0.2%)

rewrite92.0ms (2.1%)

series737.0ms (17.2%)

simplify109.0ms (2.5%)

prune262.0ms (6.1%)

localize16.0ms (0.4%)

rewrite71.0ms (1.6%)

series737.0ms (17.2%)

simplify99.0ms (2.3%)

prune208.0ms (4.8%)

localize12.0ms (0.3%)

rewrite79.0ms (1.8%)

series228.0ms (5.3%)

simplify119.0ms (2.8%)

prune340.0ms (7.9%)

regimes30.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample539.0ms (12.6%)

Profiling