Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample37.0ms (1.1%)

Algorithm

1×

intervals

Results

13.0ms	57×	body	1024	valid
8.0ms	139×	body	128	valid
6.0ms	38×	body	512	valid
3.0ms	8×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify169.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune5.0ms (0.2%)

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: 28.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.6b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
2.7b	(log.f64 (+.f64 N 1))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_79`
11×	`log-prod_binary64_165`
8×	`add-sqr-sqrt_binary64_101` `pow1_binary64_140`
6×	`add-cube-cbrt_binary64_114` `log-pow_binary64_168`
4×	`associate--l+_binary64_16` `distribute-lft-out--_binary64_31` `log-div_binary64_166` `cancel-sign-sub-inv_binary64_45`
3×	`add-exp-log_binary64_117` `associate--r+_binary64_15`
2×	`add-cbrt-cube_binary64_115` `associate--l-_binary64_17` `flip-+_binary64_53` `add-log-exp_binary64_118` `flip3-+_binary64_82` `distribute-lft-out_binary64_30`
1×	`rem-log-exp_binary64_120` `flip--_binary64_54` `difference-of-squares_binary64_48` `diff-log_binary64_171` `flip3--_binary64_83` `sub-neg_binary64_72`

Counts

2 → 44

Calls

2 calls:

9.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
4.0ms	(log.f64 (+.f64 N 1))

series75.0ms (2.3%)

Counts

2 → 6

Calls

2 calls:

50.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
24.0ms	(log.f64 (+.f64 N 1))

simplify69.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5011	673

prune164.0ms (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	5	51

Merged error: 0.1b

Counts

51 → 5

Compiler

Compiled 2088 to 1610 computations (22.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N)))
2.7b	(log.f64 (+.f64 N 1))
2.7b	(log.f64 (+.f64 N 1))
2.7b	(log.f64 (+.f64 N 1))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`log-prod_binary64_165`
21×	`*-un-lft-identity_binary64_79`
11×	`add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101`
8×	`associate--l+_binary64_16`
7×	`add-exp-log_binary64_117` `distribute-lft-in_binary64_28` `distribute-rgt-in_binary64_29` `pow1_binary64_140`
6×	`log-div_binary64_166` `add-log-exp_binary64_118` `associate--r+_binary64_15`
5×	`distribute-lft-out_binary64_30`
4×	`add-cbrt-cube_binary64_115`
3×	`rem-log-exp_binary64_120` `flip-+_binary64_53` `log-pow_binary64_168` `flip3-+_binary64_82`
1×	`flip--_binary64_54` `difference-of-squares_binary64_48` `diff-log_binary64_171` `flip3--_binary64_83` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72`

Counts

4 → 72

Calls

4 calls:

9.0ms	(-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N)))
4.0ms	(log.f64 (+.f64 N 1))
4.0ms	(log.f64 (+.f64 N 1))
4.0ms	(log.f64 (+.f64 N 1))

series191.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N)))
24.0ms	(log.f64 (+.f64 N 1))
24.0ms	(log.f64 (+.f64 N 1))
22.0ms	(log.f64 (+.f64 N 1))

simplify72.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5167	1375

prune136.0ms (4.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	83	6	89

Merged error: 0.1b

Counts

89 → 6

Compiler

Compiled 2707 to 1720 computations (36.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N))
2.7b	(log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1))))
2.7b	(log.f64 (cbrt.f64 (+.f64 N 1)))
21.0b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1)))) (-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N)))

rewrite73.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`pow1_binary64_140`
43×	`*-un-lft-identity_binary64_79`
39×	`log-pow_binary64_168`
28×	`cbrt-div_binary64_111`
26×	`log-prod_binary64_165`
20×	`log-div_binary64_166`
18×	`distribute-lft-out_binary64_30`
16×	`distribute-lft-out--_binary64_31`
15×	`flip-+_binary64_53` `add-sqr-sqrt_binary64_101` `flip3-+_binary64_82`
14×	`associate--l+_binary64_16`
13×	`add-cube-cbrt_binary64_114`
12×	`cbrt-prod_binary64_110` `associate-+r+_binary64_11`
8×	`add-exp-log_binary64_117` `frac-times_binary64_89` `associate-+l-_binary64_14` `cancel-sign-sub-inv_binary64_45`
7×	`pow-prod-down_binary64_150` `pow1/3_binary64_161`
5×	`add-log-exp_binary64_118`
4×	`add-cbrt-cube_binary64_115` `associate-l/_binary64_22` `associate-r/_binary64_21`
3×	`rem-log-exp_binary64_120` `associate--r+_binary64_15`
2×	`associate--l-_binary64_17` `sum-log_binary64_170` `pow-prod-up_binary64_149` `pow-sqr_binary64_52` `diff-log_binary64_171` `sub-neg_binary64_72`
1×	`associate-+l+_binary64_12` `+-commutative_binary64_9` `flip--_binary64_54` `associate-+r-_binary64_13` `prod-exp_binary64_128` `difference-of-squares_binary64_48` `flip3--_binary64_83` `pow-plus_binary64_142` `pow2_binary64_160`

Counts

4 → 127

Calls

4 calls:

27.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1)))) (-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N)))
11.0ms	(log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1))))
10.0ms	(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N))
5.0ms	(log.f64 (cbrt.f64 (+.f64 N 1)))

series317.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1)))) (-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N)))
70.0ms	(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N))
62.0ms	(log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1))))
56.0ms	(log.f64 (cbrt.f64 (+.f64 N 1)))

simplify72.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5136	2324

prune172.0ms (5.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	139	6	145

Merged error: 0.1b

Counts

145 → 6

Compiler

Compiled 3100 to 2267 computations (26.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
2.8b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_79`
24×	`times-frac_binary64_85`
19×	`add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101`
16×	`log-prod_binary64_165`
7×	`add-exp-log_binary64_117` `distribute-lft-out_binary64_30`
4×	`add-cbrt-cube_binary64_115` `associate-/l*_binary64_24`
3×	`associate-/r*_binary64_23` `pow1_binary64_140`
2×	`rem-log-exp_binary64_120` `div-exp_binary64_130` `div-inv_binary64_76` `add-log-exp_binary64_118` `associate-/l/_binary64_26`
1×	`cbrt-undiv_binary64_113` `flip-+_binary64_53` `log-div_binary64_166` `clear-num_binary64_78` `log-pow_binary64_168` `flip3-+_binary64_82` `frac-2neg_binary64_90`

Counts

2 → 60

Calls

2 calls:

6.0ms	(/.f64 (+.f64 N 1) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

series109.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

67.0ms	(/.f64 (+.f64 N 1) N)
42.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify75.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5428	940

prune80.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	2	2
Picked	1	0	1
Done	2	1	3
Total	67	5	72

Merged error: 0.1b

Counts

72 → 5

Compiler

Compiled 1256 to 870 computations (30.7% saved)

regimes23.0ms (0.7%)

Compiler: Compiled 99 to 70 computations (29.3% saved)

bsearch13.0ms (0.4%)

Steps

Iters	Range		Point
6	2029.7122534749428	11446.769845950132	5723.256773123576

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	46
1	50	46

end0.0ms (0%)

sample1.3s (40%)

Algorithm

1×

intervals

Results

501.0ms	2112×	body	1024	valid
253.0ms	4176×	body	128	valid
142.0ms	952×	body	512	valid
106.0ms	264×	body	2048	valid
45.0ms	496×	body	256	valid

Compiler

Compiled 135 to 98 computations (27.4% saved)

Details

analyze2.0ms (0.1%)

sample37.0ms (1.1%)

simplify169.0ms (5.2%)

prune5.0ms (0.2%)

localize6.0ms (0.2%)

rewrite16.0ms (0.5%)

series75.0ms (2.3%)

simplify69.0ms (2.1%)

prune164.0ms (5%)

localize11.0ms (0.3%)

rewrite31.0ms (0.9%)

series191.0ms (5.9%)

simplify72.0ms (2.2%)

prune136.0ms (4.2%)

localize12.0ms (0.4%)

rewrite73.0ms (2.3%)

series317.0ms (9.7%)

simplify72.0ms (2.2%)

prune172.0ms (5.3%)

localize5.0ms (0.1%)

rewrite17.0ms (0.5%)

series109.0ms (3.3%)

simplify75.0ms (2.3%)

prune80.0ms (2.5%)

regimes23.0ms (0.7%)

bsearch13.0ms (0.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (40%)

Profiling