Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample23.0ms (0.1%)

Algorithm

1×

intervals

Results

8.0ms	65×	body	1024	valid
4.0ms	132×	body	128	valid
3.0ms	32×	body	512	valid
1.0ms	8×	body	2048	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

prune7.0ms (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: 30.9b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
4.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite85.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64`
88×	`times-frac_binary64`
85×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
34×	`cancel-sign-sub-inv_binary64`
27×	`distribute-lft-out_binary64`
22×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
11×	`associate-/r*_binary64`
9×	`difference-of-sqr-1_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
6×	`associate-/r/_binary64`
5×	`add-log-exp_binary64`
3×	`pow1_binary64` `flip3--_binary64` `div-inv_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-sub_binary64`

Counts

3 → 147

Calls

3 calls:

46.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
10.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))

series133.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

81.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
27.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
25.0ms	(/.f64 x (+.f64 x 1))

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5377	2774

prune992.0ms (4.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	150	6	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	6	157

Merged error: 0.1b

Counts

157 → 6

Compiler

Compiled 17832 to 13458 computations (24.5% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.2b	(/.f64 -1 (*.f64 x x))
0.3b	(/.f64 3 (pow.f64 x 3))
6.4b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite107.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64`
68×	`times-frac_binary64`
44×	`add-sqr-sqrt_binary64`
40×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64` `unpow3_binary64`
13×	`associate-/r*_binary64` `cancel-sign-sub-inv_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-log-exp_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64`
8×	`distribute-rgt-out_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`div-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `cube-mult_binary64`
3×	`cbrt-undiv_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `frac-add_binary64` `distribute-rgt1-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 141

Calls

4 calls:

48.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
32.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
6.0ms	(/.f64 3 (pow.f64 x 3))
5.0ms	(/.f64 -1 (*.f64 x x))

series250.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
59.0ms	(/.f64 3 (pow.f64 x 3))
35.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
33.0ms	(/.f64 -1 (*.f64 x x))

simplify95.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4965	2438
1	4965	2438

prune205.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	152	7	159

Merged error: 0.1b

Counts

159 → 7

Compiler

Compiled 3587 to 2567 computations (28.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (/.f64 (+.f64 x (.f64 (+.f64 x 1) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (-.f64 x 1))))
0.0b	(pow.f64 (/.f64 x (+.f64 x 1)) 3)
0.0b	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
4.4b	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))

rewrite614.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

1199×	`*-un-lft-identity_binary64`
807×	`times-frac_binary64`
637×	`add-sqr-sqrt_binary64`
386×	`unpow-prod-down_binary64` `cube-prod_binary64`
281×	`distribute-lft-out--_binary64`
212×	`difference-of-squares_binary64`
194×	`distribute-lft-out_binary64`
153×	`add-cube-cbrt_binary64`
77×	`associate-/l*_binary64`
74×	`cancel-sign-sub-inv_binary64`
63×	`sqr-pow_binary64`
17×	`associate-/r/_binary64`
16×	`difference-of-sqr-1_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`div-inv_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `cube-div_binary64` `flip--_binary64`
5×	`difference-cubes_binary64`
4×	`rem-cube-cbrt_binary64` `pow-exp_binary64`
3×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r*_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `div-exp_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `frac-sub_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 636

Calls

4 calls:

207.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (/.f64 (+.f64 x (.f64 (+.f64 x 1) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (-.f64 x 1))))
162.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
18.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
9.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 3)

series480.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

276.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (/.f64 (+.f64 x (.f64 (+.f64 x 1) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (-.f64 x 1))))
144.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
31.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
30.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 3)

simplify384.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

648 → 648

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5002	44132

prune4.8s (23%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	646	2	648
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	648	7	655

Merged error: 0.0b

Counts

655 → 7

Compiler

Compiled 46033 to 34444 computations (25.2% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 6)
0.1b	(pow.f64 (/.f64 x (+.f64 x 1)) 6)
0.1b	(pow.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) 3)
4.3b	(-.f64 (pow.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) 3) (pow.f64 (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3) 3))

rewrite908.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Rules

1018×	`*-un-lft-identity_binary64`
844×	`unpow-prod-down_binary64`
792×	`cube-prod_binary64`
612×	`add-sqr-sqrt_binary64`
568×	`times-frac_binary64`
236×	`difference-of-squares_binary64`
233×	`distribute-lft-out--_binary64`
178×	`distribute-lft-out_binary64`
154×	`cancel-sign-sub-inv_binary64`
112×	`add-cube-cbrt_binary64`
92×	`sqr-pow_binary64`
20×	`difference-of-sqr-1_binary64` `associate-/r/_binary64`
14×	`add-exp-log_binary64`
10×	`div-inv_binary64` `pow-exp_binary64`
9×	`pow-unpow_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `cube-div_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`
5×	`flip3-+_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
4×	`pow-to-exp_binary64`
3×	`pow-pow_binary64` `div-exp_binary64`
1×	`difference-cubes_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-cube-cbrt_binary64` `frac-sub_binary64`

Counts

4 → 699

Calls

4 calls:

588.0ms	(-.f64 (pow.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) 3) (pow.f64 (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3) 3))
16.0ms	(pow.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) 3)
13.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 6)
9.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 6)

series812.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

712.0ms	(-.f64 (pow.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) 3) (pow.f64 (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3) 3))
36.0ms	(pow.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) 3)
33.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 6)
31.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 6)

simplify254.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

711 → 711

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5539	27976

prune9.4s (45.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	709	2	711
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	711	7	718

Merged error: 0.0b

Counts

718 → 7

Compiler

Compiled 69777 to 54427 computations (22% saved)

regimes48.0ms (0.2%)

Compiler: Compiled 350 to 277 computations (20.9% saved)

bsearch39.0ms (0.2%)

Steps

Iters	Range		Point
10	1584.1524704958279	404963257122649.56	11590.070419700669
9	-37135288.514302686	-398.0240890164179	-10839.340380926727

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	84
1	91	84

end0.0ms (0%)

sample996.0ms (4.8%)

Algorithm

1×

intervals

Results

253.0ms	2041×	body	1024	valid
147.0ms	4300×	body	128	valid
86.0ms	959×	body	512	valid
32.0ms	511×	body	256	valid
31.0ms	189×	body	2048	valid

Compiler

Compiled 419 to 327 computations (22% saved)

Details

analyze4.0ms (0%)

sample23.0ms (0.1%)

simplify79.0ms (0.4%)

prune7.0ms (0%)

localize7.0ms (0%)

rewrite85.0ms (0.4%)

series133.0ms (0.6%)

simplify76.0ms (0.4%)

prune992.0ms (4.7%)

localize9.0ms (0%)

rewrite107.0ms (0.5%)

series250.0ms (1.2%)

simplify95.0ms (0.5%)

prune205.0ms (1%)

localize17.0ms (0.1%)

rewrite614.0ms (2.9%)

series480.0ms (2.3%)

simplify384.0ms (1.8%)

prune4.8s (23%)

localize29.0ms (0.1%)

rewrite908.0ms (4.3%)

series812.0ms (3.9%)

simplify254.0ms (1.2%)

prune9.4s (45.1%)

regimes48.0ms (0.2%)

bsearch39.0ms (0.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample996.0ms (4.8%)

Profiling