Details

Time bar (total: 26.3s)

sample383.0ms

Algorithm
intervals
Results
163.0ms83×body1280valid
59.0ms68×body640valid
15.0ms21×body320valid
14.0ms76×body80valid
3.0ms8×body160valid

simplify41.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize65.0ms

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))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
36×times-frac
30×*-un-lft-identity add-cube-cbrt
15×associate-*r* associate-*l*
12×associate-/l*
10×add-cbrt-cube add-exp-log
5×pow1 *-commutative unswap-sqr
3×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv cos-sum div-exp prod-exp cbrt-unprod
1×+-commutative clear-num frac-2neg pow-prod-down div-inv
Counts
3 → 101
Calls
3 calls:
10.0ms
(* r (sin b))
23.0ms
(/ (* r (sin b)) (cos (+ a b)))
15.0ms
(cos (+ a b))

series196.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(* r (sin b))
112.0ms
(/ (* r (sin b)) (cos (+ a b)))
32.0ms
(cos (+ a b))

simplify2.7s

Counts
110 → 110
Iterations
IterNodes
done5001
34587
21154
1367
0163

prune602.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite364.0ms

Algorithm
rewrite-expression-head
Rules
378×add-sqr-sqrt
244×*-un-lft-identity
173×associate-*l*
144×prod-diff
132×times-frac add-cube-cbrt
117×associate-*r*
95×unswap-sqr
56×distribute-lft-out-- difference-of-squares
39×*-commutative
13×add-cbrt-cube add-exp-log
12×fma-neg associate-/l*
11×associate-/r*
8×pow1
6×add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult insert-posit16 log1p-expm1-u
3×prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down frac-sub flip-- sub-div
1×clear-num sub-neg frac-2neg diff-log div-inv
Counts
4 → 400
Calls
4 calls:
157.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
11.0ms
(* r (sin b))
15.0ms
(* (sin b) (sin a))
144.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

series604.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
56.0ms
(* r (sin b))
64.0ms
(* (sin b) (sin a))
368.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify2.3s

Counts
412 → 412
Iterations
IterNodes
done5003
22848
11103
0486

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
167×add-sqr-sqrt
125×*-un-lft-identity
84×times-frac
69×add-cube-cbrt
56×associate-*l*
42×associate-*r*
36×prod-diff
28×distribute-lft-out-- difference-of-squares unswap-sqr
14×*-commutative
13×add-cbrt-cube add-exp-log
12×fma-neg associate-/l*
8×pow1
7×associate-/r* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×prod-exp cbrt-unprod
2×cbrt-undiv flip3-- diff-log div-exp pow-prod-down associate-/r/ flip--
1×log1p-udef clear-num sub-neg frac-2neg div-inv sin-mult
Counts
4 → 233
Calls
4 calls:
55.0ms
(- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a)))))
12.0ms
(* r (sin b))
23.0ms
(* (sin b) (sin a))
114.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a))))))

series684.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a)))))
54.0ms
(* r (sin b))
69.0ms
(* (sin b) (sin a))
378.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a))))))

simplify2.1s

Counts
245 → 245
Iterations
IterNodes
done5137
22302
1757
0322

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
54×add-sqr-sqrt
48×times-frac
38×add-cube-cbrt
24×associate-*r* associate-*l*
15×add-cbrt-cube add-exp-log
13×distribute-lft-out
12×associate-/l*
10×pow1
8×*-commutative unswap-sqr
4×expm1-log1p-u associate-/r* prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down sin-mult
2×cbrt-undiv div-exp associate-/r/
1×clear-num frac-2neg flip3-+ flip-+ div-inv
Counts
4 → 149
Calls
4 calls:
53.0ms
(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (log1p (expm1 (* (sin b) (sin a)))) 1))) (fma (- (log1p (expm1 (* (sin b) (sin a))))) 1 (* (log1p (expm1 (* (sin b) (sin a)))) 1))))
22.0ms
(* (sin b) (sin a))
19.0ms
(* (sin b) (sin a))
14.0ms
(* (sin b) (sin a))

series915.0ms

Counts
4 → 12
Calls
4 calls:
697.0ms
(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (log1p (expm1 (* (sin b) (sin a)))) 1))) (fma (- (log1p (expm1 (* (sin b) (sin a))))) 1 (* (log1p (expm1 (* (sin b) (sin a)))) 1))))
71.0ms
(* (sin b) (sin a))
72.0ms
(* (sin b) (sin a))
73.0ms
(* (sin b) (sin a))

simplify2.1s

Counts
161 → 161
Iterations
IterNodes
done5002
21451
1474
0194

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0b

regimes320.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done32
232
130
019

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.1s2839×body1280valid
2.1s1837×body640valid
411.0ms766×body320valid
360.0ms2216×body80valid
128.0ms344×body160valid