Details

Time bar (total: 21.2s)

sample311.0ms

Algorithm
intervals
Results
154.0ms83×body1280valid
60.0ms68×body640valid
13.0ms76×body80valid
13.0ms21×body320valid
3.0ms8×body160valid

simplify74.0ms

Counts
1 → 1
Iterations
IterNodes
done20
520
419
317
214
112
08

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize39.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
3.0b
(cos (+ a b))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1
3×expm1-log1p-u associate-/r* times-frac associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×cos-sum clear-num frac-2neg pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 56
Calls
3 calls:
8.0ms
(* r (sin b))
12.0ms
(/ (* r (sin b)) (cos (+ a b)))
15.0ms
(cos (+ a b))

series275.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(* r (sin b))
168.0ms
(/ (* r (sin b)) (cos (+ a b)))
44.0ms
(cos (+ a b))

simplify1.9s

Counts
65 → 65
Iterations
IterNodes
done5070
32428
2611
1223
0101

prune366.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin 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))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult insert-posit16 log1p-expm1-u
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×clear-num sub-neg frac-2neg fma-neg diff-log prod-diff div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
23.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms
(* r (sin b))
31.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms
(* (sin a) (sin b))

series619.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
55.0ms
(* r (sin b))
376.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
76.0ms
(* (sin a) (sin b))

simplify1.6s

Counts
102 → 102
Iterations
IterNodes
done5001
21162
1394
0157

prune719.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
0.1b
(* r (sin b))
0.2b
(* (sin a) (sin b))
0.2b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
11×*-un-lft-identity add-cube-cbrt
8×pow1
7×add-log-exp
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* times-frac prod-diff prod-exp cbrt-unprod
2×cbrt-undiv flip3-- diff-log div-exp pow-prod-down associate-/r/ *-commutative flip-- unswap-sqr
1×log1p-udef clear-num sub-neg frac-2neg fma-neg div-inv sin-mult associate-/l*
Counts
4 → 89
Calls
4 calls:
21.0ms
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
16.0ms
(* r (sin b))
22.0ms
(* (sin a) (sin b))
43.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))

series702.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
47.0ms
(* r (sin b))
72.0ms
(* (sin a) (sin b))
408.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))

simplify1.9s

Counts
101 → 101
Iterations
IterNodes
done5000
21196
1397
0168

prune873.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin a) (sin b))
0.2b
(* (sin a) (sin b))
0.2b
(* (sin a) (sin b))
0.2b
(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (log1p (expm1 (* (sin a) (sin b)))) 1))) (fma (- (log1p (expm1 (* (sin a) (sin b))))) 1 (* (log1p (expm1 (* (sin a) (sin b)))) 1))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
15×add-cbrt-cube add-exp-log
12×add-cube-cbrt
10×pow1
9×associate-*r* associate-*l*
4×expm1-log1p-u associate-/r* times-frac prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down *-commutative sin-mult unswap-sqr
2×cbrt-undiv div-exp associate-/r/ distribute-lft-out
1×clear-num frac-2neg flip3-+ flip-+ div-inv associate-/l*
Counts
4 → 94
Calls
4 calls:
12.0ms
(* (sin a) (sin b))
11.0ms
(* (sin a) (sin b))
11.0ms
(* (sin a) (sin b))
16.0ms
(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (log1p (expm1 (* (sin a) (sin b)))) 1))) (fma (- (log1p (expm1 (* (sin a) (sin b))))) 1 (* (log1p (expm1 (* (sin a) (sin b)))) 1))))

series1.3s

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (sin a) (sin b))
84.0ms
(* (sin a) (sin b))
52.0ms
(* (sin a) (sin b))
1.1s
(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (log1p (expm1 (* (sin a) (sin b)))) 1))) (fma (- (log1p (expm1 (* (sin a) (sin b))))) 1 (* (log1p (expm1 (* (sin a) (sin b)))) 1))))

simplify1.9s

Counts
106 → 106
Iterations
IterNodes
done5000
21083
1316
0122

prune756.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes417.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done32
232
130
019

end0.0ms

sample7.1s

Algorithm
intervals
Results
3.8s2839×body1280valid
2.0s1837×body640valid
521.0ms2216×body80valid
423.0ms766×body320valid
123.0ms344×body160valid