Details

sample1.0s

Algorithm

intervals

Results

554.0ms	92×	body	10240	exit
261.0ms	70×	body	1280	valid
67.0ms	55×	body	640	valid
19.0ms	31×	body	320	valid
17.0ms	88×	body	80	valid
4.0ms	12×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize455.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 43

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
8.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series275.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
135.0ms	(expm1 (sin (expm1 a)))
124.0ms	(sin (expm1 a))
14.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
5	2343
4	983
3	411
2	204
1	118
0	74

prune483.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 32.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
39.2b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`log-prod`
1×	`rem-log-exp` `sin-diff` `expm1-udef` `rem-exp-log`

Counts

4 → 53

Calls

4 calls:

4.0ms	(sin (expm1 a))
5.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series133.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sin (expm1 a))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
33.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify4.3s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
7	4550
6	2281
5	1105
4	544
3	290
2	171
1	119
0	81

prune543.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
39.2b	(fmod (log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`sqrt-pow1`
24×	`exp-prod`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`pow1`
18×	`sqrt-prod`
8×	`pow1/2` `swap-sqr` `pow-prod-up`
6×	`add-cbrt-cube` `associate-r` `associate-l` `pow-prod-down` `add-exp-log` `pow-sqr` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`rem-exp-log`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 99

Calls

4 calls:

2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
25.0ms	(* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
0.0ms	(fmod (log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series125.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
55.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.0ms	(* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
3.0ms	(fmod (log (* (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify3.9s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
4	3687
3	827
2	323
1	166
0	94

prune691.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
39.2b	(fmod (log (* (sqrt (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (* (sqrt (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))))) a)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`exp-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-exp-log`

Counts

4 → 52

Calls

4 calls:

4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(fmod (log (* (sqrt (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (* (sqrt (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))))) a)

series156.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
60.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
58.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
6.0ms	(fmod (log (* (sqrt (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (* (sqrt (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))))) a)

simplify3.8s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
6	1422
5	651
4	266
3	130
2	84
1	56
0	40

prune514.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 32.1b

regimes510.0ms

Accuracy

0% (2.1b remaining)

Error of 33.8b against oracle of 31.7b and baseline of 33.8b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	16
1	16
0	14

end0.0ms

sample22.3s

Algorithm

intervals

Results

11.0s	2483×	body	10240	exit
7.7s	2273×	body	1280	valid
2.1s	1686×	body	640	valid
581.0ms	2763×	body	80	valid
515.0ms	829×	body	320	valid
209.0ms	443×	body	160	valid
35.0ms	5×	body	5120	valid
4.0ms	1×	body	2560	valid