Details

analyze125.0ms (0.1%)

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%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample24.0ms (0%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify171.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4915	43
1	4915	43

prune4.0ms (0%)

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: 0.2b

Counts

2 → 1

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.8b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_2828` `add-exp-log_binary64_2844` `*-un-lft-identity_binary64_2806` `pow1_binary64_2867`
14×	`add-cbrt-cube_binary64_2842`
10×	`add-cube-cbrt_binary64_2841` `associate-r_binary64_2746`
6×	`cancel-sign-sub-inv_binary64_2772` `distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `add-log-exp_binary64_2845` `pow-prod-down_binary64_2877`
4×	`associate-*r/_binary64_2748`
3×	`pow-unpow_binary64_2883` `unpow-prod-down_binary64_2885`
2×	`associate-l_binary64_2747` `*-commutative_binary64_2737` `associate-+r+_binary64_2738` `sub-neg_binary64_2799` `flip-+_binary64_2780` `flip3-+_binary64_2809` `difference-of-squares_binary64_2775` `unswap-sqr_binary64_2774`
1×	`pow-exp_binary64_2874` `distribute-lft-out_binary64_2757` `flip3--_binary64_2810` `distribute-lft-out--_binary64_2758` `pow-pow_binary64_2878` `pow-to-exp_binary64_2875` `sum-log_binary64_2897` `flip--_binary64_2781` `sqr-pow_binary64_2778` `unpow2_binary64_2871` `+-commutative_binary64_2736`

Counts

4 → 87

Calls

4 calls:

11.0ms	(.f64 (.f64 a a) (-.f64 1 a))
9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
9.0ms	(.f64 (.f64 b b) (+.f64 3 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series670.0ms (0.4%)

Counts

4 → 45

Calls

4 calls:

374.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
220.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
50.0ms	(.f64 (.f64 b b) (+.f64 3 a))
26.0ms	(.f64 (.f64 a a) (-.f64 1 a))

Compiler

Compiled 2019 to 1626 computations (19.5% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5065	2513

prune216.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	3	133

Merged error: 0.0b

Counts

133 → 3

Compiler

Compiled 4382 to 2310 computations (47.3% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.8b	(.f64 (.f64 b b) (+.f64 3 a))
3.6b	(.f64 (.f64 b b) (*.f64 a a))

rewrite67.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_2867`
32×	`associate-*r/_binary64_2748`
26×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
20×	`frac-add_binary64_2814` `pow-prod-down_binary64_2877`
14×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `flip-+_binary64_2780` `flip3-+_binary64_2809`
13×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806` `add-log-exp_binary64_2845`
11×	`associate-r_binary64_2746`
8×	`add-cube-cbrt_binary64_2841`
6×	`cancel-sign-sub-inv_binary64_2772` `distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `sum-log_binary64_2897`
5×	`flip3--_binary64_2810` `flip--_binary64_2781`
4×	`pow-prod-up_binary64_2876` `pow-plus_binary64_2869`
3×	`associate-l_binary64_2747` `*-commutative_binary64_2737` `unswap-sqr_binary64_2774`
2×	`pow-sqr_binary64_2779` `associate-+r+_binary64_2738` `sub-neg_binary64_2799` `pow2_binary64_2887` `difference-of-squares_binary64_2775`
1×	`distribute-lft-out_binary64_2757` `associate-+l+_binary64_2739` `distribute-lft-out--_binary64_2758` `+-commutative_binary64_2736`

Counts

4 → 113

Calls

4 calls:

18.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
10.0ms	(.f64 (.f64 a a) (-.f64 1 a))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))
9.0ms	(.f64 (.f64 b b) (+.f64 3 a))

series550.0ms (0.4%)

Counts

4 → 33

Calls

4 calls:

377.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
86.0ms	(.f64 (.f64 b b) (*.f64 a a))
58.0ms	(.f64 (.f64 b b) (+.f64 3 a))
29.0ms	(.f64 (.f64 a a) (-.f64 1 a))

Compiler

Compiled 1803 to 1444 computations (19.9% saved)

simplify124.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4951	5208
1	4951	5208

prune341.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	146	3	149

Merged error: 0b

Counts

149 → 3

Compiler

Compiled 7168 to 4080 computations (43.1% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)
0.8b	(.f64 (.f64 b b) (+.f64 3 a))
29.0b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806`
15×	`add-exp-log_binary64_2844` `pow1_binary64_2867`
14×	`add-cbrt-cube_binary64_2842`
12×	`add-cube-cbrt_binary64_2841`
10×	`associate-r_binary64_2746`
7×	`cbrt-prod_binary64_2837`
6×	`cancel-sign-sub-inv_binary64_2772` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unpow-prod-down_binary64_2885` `pow-prod-down_binary64_2877`
5×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756`
4×	`add-log-exp_binary64_2845` `associate-*r/_binary64_2748`
3×	`pow-unpow_binary64_2883`
2×	`associate-l_binary64_2747` `*-commutative_binary64_2737` `sub-neg_binary64_2799` `sqr-pow_binary64_2778` `difference-of-squares_binary64_2775` `unswap-sqr_binary64_2774`
1×	`pow-exp_binary64_2874` `pow1/3_binary64_2888` `distribute-lft-out_binary64_2757` `flip3--_binary64_2810` `distribute-lft-out--_binary64_2758` `pow-pow_binary64_2878` `pow-to-exp_binary64_2875` `flip-+_binary64_2780` `flip--_binary64_2781` `flip3-+_binary64_2809`

Counts

4 → 88

Calls

4 calls:

10.0ms	(.f64 (.f64 a a) (-.f64 1 a))
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
8.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6))

series357.0ms (0.2%)

Counts

4 → 34

Calls

4 calls:

221.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6))
54.0ms	(.f64 (.f64 b b) (+.f64 3 a))
53.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)
28.0ms	(.f64 (.f64 a a) (-.f64 1 a))

Compiler

Compiled 1754 to 1363 computations (22.3% saved)

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5167	1639

prune180.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	122	3	125

Merged error: 0b

Counts

125 → 3

Compiler

Compiled 4161 to 2213 computations (46.8% saved)

localize41.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1))
1.0b	(.f64 (.f64 b b) (-.f64 9 (*.f64 a a)))
2.9b	(+.f64 (.f64 (.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 a 8) (.f64 (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))))) (.f64 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1))) (.f64 4 (-.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2))))))
39.8b	(/.f64 (+.f64 (.f64 (.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 a 8) (.f64 (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))))) (.f64 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1))) (.f64 4 (-.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))))) (.f64 (.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2)))))

rewrite13.2s (8.8%)

Algorithm

1×	rewrite-expression-head

Rules

32754×	`associate-*r/_binary64_2748`
28080×	`frac-times_binary64_2816`
20384×	`frac-add_binary64_2814`
18194×	`flip3--_binary64_2810` `flip--_binary64_2781`
14040×	`associate-*l/_binary64_2749`
11258×	`flip-+_binary64_2780` `flip3-+_binary64_2809`
5202×	`associate-/l/_binary64_2753`
27×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
26×	`associate-/r/_binary64_2752`
21×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756`
18×	`pow1_binary64_2867`
16×	`cancel-sign-sub-inv_binary64_2772` `associate-+r+_binary64_2738`
14×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806`
12×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `add-cube-cbrt_binary64_2841`
9×	`pow-prod-down_binary64_2877`
8×	`sub-neg_binary64_2799` `associate-r_binary64_2746`
6×	`add-log-exp_binary64_2845`
4×	`associate-+l+_binary64_2739`
3×	`times-frac_binary64_2812` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `associate-/l*_binary64_2751`
2×	`associate-l_binary64_2747` `*-commutative_binary64_2737`
1×	`div-inv_binary64_2803` `distribute-lft-out_binary64_2757` `associate-/r*_binary64_2750` `sum-log_binary64_2897` `clear-num_binary64_2805` `difference-of-squares_binary64_2775` `unswap-sqr_binary64_2774` `frac-2neg_binary64_2817` `+-commutative_binary64_2736`

Counts

4 → 10540

Calls

4 calls:

741.0ms	(/.f64 (+.f64 (.f64 (.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 a 8) (.f64 (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))))) (.f64 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1))) (.f64 4 (-.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))))) (.f64 (.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2)))))
201.0ms	(+.f64 (.f64 (.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 a 8) (.f64 (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))))) (.f64 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1))) (.f64 4 (-.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2))))))
14.0ms	(.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1))
9.0ms	(.f64 (.f64 b b) (-.f64 9 (*.f64 a a)))

series4.2s (2.8%)

Counts

4 → 42

Calls

4 calls:

3.6s	(/.f64 (+.f64 (.f64 (.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 a 8) (.f64 (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))))) (.f64 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1))) (.f64 4 (-.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))))) (.f64 (.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2)))))
391.0ms	(+.f64 (.f64 (.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 a 8) (.f64 (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))))) (.f64 (+.f64 (.f64 a (.f64 (+.f64 a (neg.f64 (pow.f64 a 3))) (-.f64 3 a))) (.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1))) (.f64 4 (-.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2))))))
111.0ms	(.f64 (.f64 (.f64 b b) (-.f64 9 (.f64 a a))) (+.f64 a 1))
102.0ms	(.f64 (.f64 b b) (-.f64 9 (*.f64 a a)))

Compiler

Compiled 10583 to 8083 computations (23.6% saved)

simplify25.3s (16.8%)

Algorithm

1×	egg-herbie

Counts

10582 → 10582

Iterations

Useful iterations: 0 (579.0ms)

Iter	Nodes	Cost
0	27543	3887180

Details

analyze125.0ms (0.1%)

sample24.0ms (0%)

simplify171.0ms (0.1%)

prune4.0ms (0%)

localize20.0ms (0%)

rewrite43.0ms (0%)

series670.0ms (0.4%)

simplify86.0ms (0.1%)

prune216.0ms (0.1%)

localize20.0ms (0%)

rewrite67.0ms (0%)

series550.0ms (0.4%)

simplify124.0ms (0.1%)

prune341.0ms (0.2%)

localize17.0ms (0%)

rewrite40.0ms (0%)

series357.0ms (0.2%)

simplify83.0ms (0.1%)

prune180.0ms (0.1%)

localize41.0ms (0%)

rewrite13.2s (8.8%)

series4.2s (2.8%)

simplify25.3s (16.8%)

prune1.7min (69.4%)

Profiling