Details

analyze341.0ms (6.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	366	12
1	366	12
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Symmetry

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample57.0ms (1.1%)

Algorithm

1×

intervals

Results

30.0ms	65×	body	2048	valid
7.0ms	59×	body	512	valid
6.0ms	33×	body	1024	valid
3.0ms	82×	body	128	valid
1.0ms	16×	body	256	valid
0.0ms	1×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	366	12
1	366	12

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

31.5b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.1b	(-.f64 1 (cos.f64 x))
15.3b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite71.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

30.8b

Rules

14×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
7×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
6×	`times-frac_binary64_84` `difference-of-squares_binary64_47` `associate-/l*_binary64_23`
5×	`add-cube-cbrt_binary64_113`
4×	`add-log-exp_binary64_117`
3×	`distribute-lft-out--_binary64_30` `cancel-sign-sub-inv_binary64_44`
2×	`pow1_binary64_139` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `flip3--_binary64_82` `associate-/l/_binary64_25` `flip--_binary64_53`
1×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `div-sub_binary64_83` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/r*_binary64_22` `diff-log_binary64_170` `sub-neg_binary64_71`

Counts

2 → 47

Calls

2 calls:

8.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 708 to 357 computations (49.6% saved)

series72.0ms (1.4%)

Error

0.3b

Counts

2 → 12

Calls

2 calls:

41.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
20.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 320 to 251 computations (21.6% saved)

simplify63.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	6299	811

prune57.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	51	8	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	8	60

Error

0.0b

Counts

60 → 8

Compiler

Compiled 872 to 480 computations (45% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.5b	(+.f64 1 (cos.f64 x))
15.1b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite142.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
24×	`*-un-lft-identity_binary64_78`
22×	`times-frac_binary64_84`
16×	`add-sqr-sqrt_binary64_100`
14×	`add-cube-cbrt_binary64_113`
12×	`div-exp_binary64_129` `cbrt-undiv_binary64_112`
11×	`pow1_binary64_139` `associate-/l*_binary64_23`
7×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111`
6×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
5×	`distribute-lft-out_binary64_29` `associate-/r*_binary64_22`
4×	`div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52`
3×	`sqr-sin-a_binary64_226` `div-sub_binary64_83` `swap-sqr_binary64_45` `associate-l_binary64_19` `associate-r_binary64_18`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l/_binary64_25` `sin-mult_binary64_233`
1×	`sum-log_binary64_169` `+-commutative_binary64_8` `pow2_binary64_159` `pow-prod-down_binary64_149` `pow-prod-up_binary64_148` `pow-plus_binary64_141` `pow-sqr_binary64_51` `unswap-sqr_binary64_46` `*-commutative_binary64_9`

Counts

4 → 111

Calls

4 calls:

11.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
8.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
6.0ms	(+.f64 1 (cos.f64 x))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))

Compiler

Compiled 2503 to 957 computations (61.8% saved)

series207.0ms (4.1%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

82.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
61.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
28.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
17.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 870 to 613 computations (29.5% saved)

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4936	1964
1	4936	1964

prune117.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Error

0.0b

Counts

143 → 7

Compiler

Compiled 2348 to 1191 computations (49.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.1b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

rewrite103.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`add-sqr-sqrt_binary64_100`
22×	`times-frac_binary64_84`
21×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
13×	`associate-l_binary64_19`
6×	`div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111` `tan-quot_binary64_237` `associate-/l*_binary64_23`
3×	`add-log-exp_binary64_117` `div-inv_binary64_75` `associate-r_binary64_18` `associate-/l/_binary64_25`
2×	`frac-times_binary64_88` `unswap-sqr_binary64_46` `associate-l/_binary64_21` `associate-r/_binary64_20` `frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`pow-prod-down_binary64_149` `*-commutative_binary64_9`

Counts

3 → 87

Calls

3 calls:

10.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
8.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
4.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 1623 to 756 computations (53.4% saved)

series211.0ms (4.2%)

Error

Counts

3 → 18

Calls

3 calls:

92.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
76.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
27.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 586 to 459 computations (21.7% saved)

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4937	1665
1	4937	1665

prune87.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	105	7	112

Error

Counts

112 → 7

Compiler

Compiled 1757 to 908 computations (48.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 x x) (+.f64 (cos.f64 x) 1))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.5b	(+.f64 (cos.f64 x) 1)
15.0b	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (*.f64 x x) (+.f64 (cos.f64 x) 1)))

rewrite113.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
16×	`pow1_binary64_139`
13×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111` `*-un-lft-identity_binary64_78`
12×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113`
7×	`associate-r_binary64_18`
6×	`div-exp_binary64_129` `add-log-exp_binary64_117` `cbrt-undiv_binary64_112`
4×	`associate-r/_binary64_20` `pow-prod-down_binary64_149` `associate-l*_binary64_19`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `swap-sqr_binary64_45`
2×	`sqr-sin-a_binary64_226` `sin-mult_binary64_233` `associate-/r/_binary64_24` `distribute-lft-out_binary64_29` `unswap-sqr_binary64_46` `*-commutative_binary64_9`
1×	`frac-2neg_binary64_89` `times-frac_binary64_84` `div-sub_binary64_83` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l/_binary64_25` `associate-/l_binary64_23` `associate-/r_binary64_22` `sum-log_binary64_169` `+-commutative_binary64_8` `pow2_binary64_159` `pow-prod-up_binary64_148` `pow-plus_binary64_141` `pow-sqr_binary64_51` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27`

Counts

4 → 92

Calls

4 calls:

14.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (*.f64 x x) (+.f64 (cos.f64 x) 1)))
8.0ms	(.f64 (.f64 x x) (+.f64 (cos.f64 x) 1))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 (cos.f64 x) 1)

Compiler

Compiled 2039 to 743 computations (63.6% saved)

series185.0ms (3.7%)

Error

Counts

4 → 24

Calls

4 calls:

83.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (*.f64 x x) (+.f64 (cos.f64 x) 1)))
35.0ms	(.f64 (.f64 x x) (+.f64 (cos.f64 x) 1))
26.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
19.0ms	(+.f64 (cos.f64 x) 1)

Compiler

Compiled 892 to 617 computations (30.8% saved)

simplify46.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5059	1555

prune88.0ms (1.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	116	7	123

Error

Counts

123 → 7

Compiler

Compiled 1958 to 896 computations (54.2% saved)

regimes198.0ms (3.9%)

Accuracy

Total 0.1b remaining (98%)

Threshold costs 0.1b (98%)

Compiler

Compiled 1953 to 1389 computations (28.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

Removed

()

end0.0ms (0%)

sample2.7s (52.8%)

Algorithm

1×

intervals

Results

879.0ms	2002×	body	2048	valid
219.0ms	1127×	body	1024	valid
189.0ms	1530×	body	512	valid
94.0ms	2498×	body	128	valid
66.0ms	754×	body	256	valid
39.0ms	89×	body	4096	valid

Compiler

Compiled 922 to 659 computations (28.5% saved)

Details

analyze341.0ms (6.8%)

sample57.0ms (1.1%)

simplify22.0ms (0.4%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite71.0ms (1.4%)

series72.0ms (1.4%)

simplify63.0ms (1.3%)

prune57.0ms (1.1%)

localize9.0ms (0.2%)

rewrite142.0ms (2.8%)

series207.0ms (4.1%)

simplify81.0ms (1.6%)

prune117.0ms (2.3%)

localize8.0ms (0.2%)

rewrite103.0ms (2%)

series211.0ms (4.2%)

simplify84.0ms (1.7%)

prune87.0ms (1.7%)

localize9.0ms (0.2%)

rewrite113.0ms (2.2%)

series185.0ms (3.7%)

simplify46.0ms (0.9%)

prune88.0ms (1.7%)

regimes198.0ms (3.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (52.8%)

Profiling