Details

sample294.0ms

Algorithm

intervals

Results

77.0ms	83×	body	1280	valid
44.0ms	72×	body	640	valid
12.0ms	61×	body	80	valid
10.0ms	24×	body	320	valid
5.0ms	16×	body	160	valid

simplify105.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize36.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.4b	(cos (+ a b))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

20.0ms	(* r (sin b))
27.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

series318.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* r (sin b))
195.0ms	(/ (* r (sin b)) (cos (+ a b)))
48.0ms	(cos (+ a b))

simplify1.1s

Counts

62 → 62

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	96	575
1	215	562
2	880	492
done	5001	482

prune500.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `associate-/l*` `sub-div`

Counts

4 → 89

Calls

4 calls:

24.0ms	(* (cos a) (cos b))
27.0ms	(* r (sin b))
61.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
27.0ms	(* (sin a) (sin b))

series696.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (cos a) (cos b))
69.0ms	(* r (sin b))
450.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
98.0ms	(* (sin a) (sin b))

simplify1.8s

Counts

101 → 101

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	165	1189
1	402	1149
2	1812	1019
done	5000	978

prune924.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 113

Calls

4 calls:

21.0ms	(* (cos a) (cos b))
149.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
63.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series861.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (cos a) (cos b))
458.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
220.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
95.0ms	(* (sin a) (sin b))

simplify2.0s

Counts

125 → 125

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	195	2025
1	479	1971
2	2063	1792
done	5000	1738

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
3.2b	(log (exp (* (sin a) (sin b))))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-l`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`log-prod` `prod-exp` `associate-/r` `log-pow` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `div-inv`
1×	`exp-prod` `exp-to-pow` `frac-2neg` `associate-*r/` `rem-log-exp` `clear-num` `sin-mult`

Counts

4 → 104

Calls

4 calls:

119.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
63.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
25.0ms	(* (sin a) (sin b))
10.0ms	(log (exp (* (sin a) (sin b))))

series856.0ms

Counts

4 → 12

Calls

4 calls:

441.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
224.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
100.0ms	(* (sin a) (sin b))
91.0ms	(log (exp (* (sin a) (sin b))))

simplify1.5s

Counts

116 → 116

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	172	2092
1	412	1832
2	1912	1666
done	5000	1659

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes553.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	14	17
1	17	13
done	17	13

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.8s	2921×	body	1280	valid
1.4s	1832×	body	640	valid
935.0ms	780×	body	320	valid
414.0ms	2130×	body	80	valid
105.0ms	341×	body	160	valid